| Publisher: AIP
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Similar Journals
|
Chaos : An Interdisciplinary Journal of Nonlinear Science
Journal Prestige (SJR): 0.716  Citation Impact (citeScore): 2 Number of Followers: 3  Hybrid journal (It can contain Open Access articles)ISSN (Print) 1054-1500 - ISSN (Online) 1089-7682 Published by AIP  [28 journals]
|
- GPU-based, interactive exploration of large spatiotemporal climate
networks-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Stefan Buschmann, Peter Hoffmann, Ankit Agarwal, Norbert Marwan, Thomas Nocke
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
This paper introduces the Graphics Processing Unit (GPU)-based tool Geo-Temporal eXplorer (GTX), integrating a set of highly interactive techniques for visual analytics of large geo-referenced complex networks from the climate research domain. The visual exploration of these networks faces a multitude of challenges related to the geo-reference and the size of these networks with up to several million edges and the manifold types of such networks. In this paper, solutions for the interactive visual analysis for several distinct types of large complex networks will be discussed, in particular, time-dependent, multi-scale, and multi-layered ensemble networks. Custom-tailored for climate researchers, the GTX tool supports heterogeneous tasks based on interactive, GPU-based solutions for on-the-fly large network data processing, analysis, and visualization. These solutions are illustrated for two use cases: multi-scale climatic process and climate infection risk networks. This tool helps one to reduce the complexity of the highly interrelated climate information and unveils hidden and temporal links in the climate system, not available using standard and linear tools (such as empirical orthogonal function analysis).
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-14T02:03:38Z
DOI: 10.1063/5.0131933
-
- Chaotic advection in a recirculating flow: Effect of a fluid
multiple-flexible-solid interaction-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Vinay Prasad, Atul Sharma, Salil S. Kulkarni
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
This paper deals with chaotic advection due to a two-way interaction between flexible elliptical-solids and a laminar lid-driven cavity flow in two dimensions. The present Fluid multiple-flexible-Solid Interaction study involves various number [math](= 1–120) of equal-sized neutrally buoyant elliptical-solids (aspect ratio [math]) such that they result in the total volume fraction [math] as in our recent study on single solid, done for non-dimensional shear modulus [math] and Reynolds number [math]. Results are presented first for flow-induced motion and deformation of the solids and later for chaotic advection of the fluid. After the initial transients, the fluid as well as solid motion (and deformation) attain periodicity for smaller [math] while they attain aperiodic states for larger [math]. Adaptive material tracking (AMT) and Finite-Time Lyapunov Exponent (FTLE)-based Lagrangian dynamical analysis revealed that the chaotic advection increases up to [math] and decreases at larger [math](= 6–10) for the periodic state. Similar analysis for the transient state revealed an asymptotic increase in the chaotic advection with increasing [math]. These findings are demonstrated with the help of two types of chaos signatures: exponential growth of material blob’s interface and Lagrangian coherent structures, revealed by the AMT and FTLE, respectively. Our work, which is relevant to several applications, presents a novel technique based on the motion of multiple deformable-solids for enhancement of chaotic advection.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-14T02:03:37Z
DOI: 10.1063/5.0132986
-
- Learning effective dynamics from data-driven stochastic systems
-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Lingyu Feng, Ting Gao, Min Dai, Jinqiao Duan
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real-world applications. This work is devoted to investigating the effective dynamics for slow–fast stochastic dynamical systems. Given observation data on a short-term period satisfying some unknown slow–fast stochastic systems, we propose a novel algorithm, including a neural network called Auto-SDE, to learn an invariant slow manifold. Our approach captures the evolutionary nature of a series of time-dependent autoencoder neural networks with the loss constructed from a discretized stochastic differential equation. Our algorithm is also validated to be accurate, stable, and effective through numerical experiments under various evaluation metrics.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-14T02:03:36Z
DOI: 10.1063/5.0126667
-
- Parsimonious physics-informed random projection neural networks for
initial value problems of ODEs and index-1 DAEs-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Gianluca Fabiani, Evangelos Galaris, Lucia Russo, Constantinos Siettos
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
We present a numerical method based on random projections with Gaussian kernels and physics-informed neural networks for the numerical solution of initial value problems (IVPs) of nonlinear stiff ordinary differential equations (ODEs) and index-1 differential algebraic equations (DAEs), which may also arise from spatial discretization of partial differential equations (PDEs). The internal weights are fixed to ones while the unknown weights between the hidden and output layer are computed with Newton’s iterations using the Moore–Penrose pseudo-inverse for low to medium scale and sparse QR decomposition with [math] regularization for medium- to large-scale systems. Building on previous works on random projections, we also prove its approximation accuracy. To deal with stiffness and sharp gradients, we propose an adaptive step-size scheme and address a continuation method for providing good initial guesses for Newton iterations. The “optimal” bounds of the uniform distribution from which the values of the shape parameters of the Gaussian kernels are sampled and the number of basis functions are “parsimoniously” chosen based on bias-variance trade-off decomposition. To assess the performance of the scheme in terms of both numerical approximation accuracy and computational cost, we used eight benchmark problems (three index-1 DAEs problems, and five stiff ODEs problems including the Hindmarsh–Rose neuronal model of chaotic dynamics and the Allen–Cahn phase-field PDE). The efficiency of the scheme was compared against two stiff ODEs/DAEs solvers, namely, ode15s and ode23t solvers of the MATLAB ODE suite as well as against deep learning as implemented in the DeepXDE library for scientific machine learning and physics-informed learning for the solution of the Lotka–Volterra ODEs included in the demos of the library. A software/toolbox in Matlab (that we call RanDiffNet) with demos is also provided.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-13T02:16:09Z
DOI: 10.1063/5.0135903
-
- Dynamics on networks with higher-order interactions
-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Z. Gao, D. Ghosh, H. A. Harrington, J. G. Restrepo, D. Taylor
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-13T02:15:59Z
DOI: 10.1063/5.0151265
-
- Deterrence through punishment can resolve collective risk dilemmas in
carbon emission games-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Luo-Luo Jiang, Zhi Chen, Matjaž Perc, Zhen Wang, Jürgen Kurths, Yamir Moreno
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
Collective risk social dilemmas are at the heart of the most pressing global challenges we are facing today, including climate change mitigation and the overuse of natural resources. Previous research has framed this problem as a public goods game (PGG), where a dilemma arises between short-term interests and long-term sustainability. In the PGG, subjects are placed in groups and asked to choose between cooperation and defection, while keeping in mind their personal interests as well as the commons. Here, we explore how and to what extent the costly punishment of defectors is successful in enforcing cooperation by means of human experiments. We show that an apparent irrational underestimation of the risk of being punished plays an important role, and that for sufficiently high punishment fines, this vanishes and the threat of deterrence suffices to preserve the commons. Interestingly, however, we find that high fines not only avert freeriders, but they also demotivate some of the most generous altruists. As a consequence, the tragedy of the commons is predominantly averted due to cooperators that contribute only their “fair share” to the common pool. We also find that larger groups require larger fines for the deterrence of punishment to have the desired prosocial effect.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-13T02:15:59Z
DOI: 10.1063/5.0147226
-
- Multi-band oscillations emerge from a simple spiking network
-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Tianyi Wu, Yuhang Cai, Ruilin Zhang, Zhongyi Wang, Louis Tao, Zhuo-Cheng Xiao
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
In the brain, coherent neuronal activities often appear simultaneously in multiple frequency bands, e.g., as combinations of alpha (8–12 Hz), beta (12.5–30 Hz), and gamma (30–120 Hz) oscillations, among others. These rhythms are believed to underlie information processing and cognitive functions and have been subjected to intense experimental and theoretical scrutiny. Computational modeling has provided a framework for the emergence of network-level oscillatory behavior from the interaction of spiking neurons. However, due to the strong nonlinear interactions between highly recurrent spiking populations, the interplay between cortical rhythms in multiple frequency bands has rarely been theoretically investigated. Many studies invoke multiple physiological timescales (e.g., various ion channels or multiple types of inhibitory neurons) or oscillatory inputs to produce rhythms in multi-bands. Here, we demonstrate the emergence of multi-band oscillations in a simple network consisting of one excitatory and one inhibitory neuronal population driven by constant input. First, we construct a data-driven, Poincaré section theory for robust numerical observations of single-frequency oscillations bifurcating into multiple bands. Then, we develop model reductions of the stochastic, nonlinear, high-dimensional neuronal network to capture the appearance of multi-band dynamics and the underlying bifurcations theoretically. Furthermore, when viewed within the reduced state space, our analysis reveals conserved geometrical features of the bifurcations on low-dimensional dynamical manifolds. These results suggest a simple geometric mechanism behind the emergence of multi-band oscillations without appealing to oscillatory inputs or multiple synaptic or neuronal timescales. Thus, our work points to unexplored regimes of stochastic competition between excitation and inhibition behind the generation of dynamic, patterned neuronal activities.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-12T03:49:27Z
DOI: 10.1063/5.0106884
-
- Random migration with tie retention promotes cooperation in the
prisoner’s dilemma game-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Zhihu Yang, Liping Zhang
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
Migration has the potential to induce outbreaks of cooperation, yet little is known about random migration. Does random migration really inhibit cooperation as often as previously thought' Besides, prior literature has often ignored the stickiness of social ties when designing migration protocols and assumed that players always immediately disconnect from their ex-neighbors once they migrate. However, this is not always true. Here, we propose a model where players can still retain some bonds with their ex-partners after they move from one place to another. The results show that maintaining a certain number of social ties, regardless of prosocial, exploitative, or punitive, can nevertheless facilitate cooperation even if migration occurs in a totally random fashion. Notably, it reflects that tie retention can help random migration, previously thought to be harmful to cooperation, restore the ability to spark bursts of cooperation. The maximum number of retained ex-neighbors plays an important role in facilitating cooperation. We analyze the impact of social diversity in terms of the maximum number of retained ex-neighbors and migration probability, and find that the former enhances cooperation while the latter often engenders an optimal dependence between cooperation and migration. Our results instantiate a scenario in which random migration yields the outbreak of cooperation and highlight the importance of social stickiness.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-12T03:49:27Z
DOI: 10.1063/5.0139874
-
- Determinants of collective failure in excitable networks
-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Uroš Barać, Matjaž Perc, Marko Gosak
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
We study collective failures in biologically realistic networks that consist of coupled excitable units. The networks have broad-scale degree distribution, high modularity, and small-world properties, while the excitable dynamics is determined by the paradigmatic FitzHugh–Nagumo model. We consider different coupling strengths, bifurcation distances, and various aging scenarios as potential culprits of collective failure. We find that for intermediate coupling strengths, the network remains globally active the longest if the high-degree nodes are first targets for inactivation. This agrees well with previously published results, which showed that oscillatory networks can be highly fragile to the targeted inactivation of low-degree nodes, especially under weak coupling. However, we also show that the most efficient strategy to enact collective failure does not only non-monotonically depend on the coupling strength, but it also depends on the distance from the bifurcation point to the oscillatory behavior of individual excitable units. Altogether, we provide a comprehensive account of determinants of collective failure in excitable networks, and we hope this will prove useful for better understanding breakdowns in systems that are subject to such dynamics.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-12T03:49:26Z
DOI: 10.1063/5.0149578
-
- Allocation of hospital beds on the emergence of new infectious disease: A
mathematical model-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: A. K. Misra, Jyoti Maurya
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
This paper is concerned to a mathematical model for the management of hospital beds when a new infection emerges in the population with the existing infections. The study of this joint dynamics presents formidable mathematical challenges due to a limited number of hospital beds. We have derived the invasion reproduction number, which investigates the potential of a newly emerged infectious disease to persist when some infectious diseases are already invaded the host population. We have shown that the proposed system exhibits transcritical, saddle-node, Hopf, and Bogdanov–Takens bifurcations under certain conditions. We have also shown that the total number of infected individuals may increase if the fraction of the total number of hospital beds is not properly allotted to the existing and a newly emerged infectious disease. The analytically obtained results are verified with the help of numerical simulations.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-12T03:49:25Z
DOI: 10.1063/5.0133703
-
- Multimodal distribution of transient time of predator extinction in a
three-species food chain-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Debarghya Pattanayak, Arindam Mishra, Nandadulal Bairagi, Syamal K. Dana
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
The transient dynamics capture the time history in the behavior of a system before reaching an attractor. This paper deals with the statistics of transient dynamics in a classic tri-trophic food chain with bistability. The species of the food chain model either coexist or undergo a partial extinction with predator death after a transient time depending upon the initial population density. The distribution of transient time to predator extinction shows interesting patterns of inhomogeneity and anisotropy in the basin of the predator-free state. More precisely, the distribution shows a multimodal character when the initial points are located near a basin boundary and a unimodal character when chosen from a location far away from the boundary. The distribution is also anisotropic because the number of modes depends on the direction of the local of initial points. We define two new metrics, viz., homogeneity index and local isotropic index, to characterize the distinctive features of the distribution. We explain the origin of such multimodal distributions and try to present their ecological implications.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-12T03:49:24Z
DOI: 10.1063/5.0136372
-
- Two new parameters for the ordinal analysis of images
-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Christoph Bandt, Katharina Wittfeld
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
Local patterns play an important role in statistical physics as well as in image processing. Two-dimensional ordinal patterns were studied by Ribeiro et al. who determined permutation entropy and complexity in order to classify paintings and images of liquid crystals. Here, we find that the [math] patterns of neighboring pixels come in three types. The statistics of these types, expressed by two parameters, contains the relevant information to describe and distinguish textures. The parameters are most stable and informative for isotropic structures.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-12T03:49:24Z
DOI: 10.1063/5.0136912
-
- Parameter and coupling estimation in small networks of Izhikevich’s
neurons-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: R. P. Aristides, A. J. Pons, H. A. Cerdeira, C. Masoller, G. Tirabassi
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
Nowadays, experimental techniques allow scientists to have access to large amounts of data. In order to obtain reliable information from the complex systems that produce these data, appropriate analysis tools are needed. The Kalman filter is a frequently used technique to infer, assuming a model of the system, the parameters of the model from uncertain observations. A well-known implementation of the Kalman filter, the unscented Kalman filter (UKF), was recently shown to be able to infer the connectivity of a set of coupled chaotic oscillators. In this work, we test whether the UKF can also reconstruct the connectivity of small groups of coupled neurons when their links are either electrical or chemical synapses. In particular, we consider Izhikevich neurons and aim to infer which neurons influence each other, considering simulated spike trains as the experimental observations used by the UKF. First, we verify that the UKF can recover the parameters of a single neuron, even when the parameters vary in time. Second, we analyze small neural ensembles and demonstrate that the UKF allows inferring the connectivity between the neurons, even for heterogeneous, directed, and temporally evolving networks. Our results show that time-dependent parameter and coupling estimation is possible in this nonlinearly coupled system.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-12T03:49:23Z
DOI: 10.1063/5.0144499
-
- Analytical predictions of periodic oscillations in a piezoelectric energy
harvester under combined aeroelastic and harmonic excitation-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Bo Yu
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
This work studies a piezoelectric energy harvester subjected to both fluid flow and harmonic excitation. A lumped parameter model that incorporates fluid–structure interaction is presented to analyze the effects of both fluid flow and harmonic excitation on the proposed harvester. The method of implicit mapping is employed to calculate the periodic displacement, voltage, and velocity oscillations. Stabilities and bifurcations of periodic oscillations are determined based on the eigenvalues of the resultant matrix of mapping structures. The displacement and voltage nodes of the proposed energy harvester varying with excitation amplitude and frequency are investigated. The maximum eigenvalue magnitudes are illustrated. Utilizing the periodic nodes of the displacement and voltage, the harmonic amplitudes and phases are calculated using the fast Fourier transform. The harmonic amplitudes of both displacement and voltage varying with excitation frequency are depicted. For the stable periodic responses, the implicit maps and numerical simulations are presented to demonstrate the effectiveness of the energy harvesting system. The theoretical analysis presented in this study can be useful for the design and optimization of the proposed energy harvester.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-10T06:28:48Z
DOI: 10.1063/5.0135032
-
- Increasing the synchronization stability in complex networks
-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Xian Wu, Kaihua Xi, Aijie Cheng, Hai Xiang Lin, Jan H. van Schuppen
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
We aim to increase the ability of coupled phase oscillators to maintain synchronization when the system is affected by stochastic disturbances. We model the disturbances by Gaussian noise and use the mean first hitting time when the state hits the boundary of a secure domain, that is a subset of the basin of attraction, to measure synchronization stability. Based on the invariant probability distribution of a system of phase oscillators subject to Gaussian disturbances, we propose an optimization method to increase the mean first hitting time and, thus, increase synchronization stability. In this method, a new metric for synchronization stability is defined as the probability of the state being absent from the secure domain, which reflects the impact of all the system parameters and the strength of disturbances. Furthermore, by this new metric, one may identify those edges that may lead to desynchronization with a high risk. A case study shows that the mean first hitting time is dramatically increased after solving corresponding optimization problems, and vulnerable edges are effectively identified. It is also found that optimizing synchronization by maximizing the order parameter or the phase cohesiveness may dramatically increase the value of the metric and decrease the mean first hitting time, thus decrease synchronization stability.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-10T06:28:48Z
DOI: 10.1063/5.0114974
-
- Complexity of couplings in multivariate time series via ordinal persistent
homology-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Taichi Haruna
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
We propose a new measure of the complexity of couplings in multivariate time series by combining the techniques of ordinal pattern analysis and topological data analysis. We construct an increasing sequence of simplicial complexes encoding the information about couplings among the components of a given multivariate time series through the intersection of ordinal patterns. The complexity measure is then defined by making use of the persistent homology groups. We validate the complexity measure both theoretically and numerically.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-10T06:28:47Z
DOI: 10.1063/5.0136772
-
- Collective behavior of identical Stuart–Landau oscillators in a star
network with coupling asymmetry effects-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: XinYue Chen, Ran Chen, YiLin Sun, Shuai Liu
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
In this study, we investigated the impact of the asymmetry of a coupling scheme on oscillator dynamics in a star network. We obtained stability conditions for the collective behavior of the systems, ranging from an equilibrium point over complete synchronization (CS) and quenched hub incoherence to remote synchronization states using both numerical and analytical methods. The coupling asymmetry factor [math] significantly influences and determines the stable parameter region of each state. For [math], the equilibrium point can emerge when the Hopf bifurcation parameter [math] is positive, which is impossible for diffusive coupling. However, CS can occur even if [math] is negative under [math]. Unlike diffusive coupling, we observe more behavior when [math], including additional in-phase remote synchronization. These results are supported by theoretical analysis and validated through numerical simulations and independent of network size. The findings may offer practical methods for controlling, restoring, or obstructing specific collective behavior.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-10T06:28:45Z
DOI: 10.1063/5.0142904
-
- The hidden complexity of a double-scroll attractor: Analytic proofs from a
piecewise-smooth system-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Vladimir N. Belykh, Nikita V. Barabash, Igor Belykh
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
Double-scroll attractors are one of the pillars of modern chaos theory. However, rigorous computer-free analysis of their existence and global structure is often elusive. Here, we address this fundamental problem by constructing an analytically tractable piecewise-smooth system with a double-scroll attractor. We derive a Poincaré return map to prove the existence of the double-scroll attractor and explicitly characterize its global dynamical properties. In particular, we reveal a hidden set of countably many saddle orbits associated with infinite-period Smale horseshoes. These complex hyperbolic sets emerge from an ordered iterative process that yields sequential intersections between different horseshoes and their preimages. This novel distinctive feature differs from the classical Smale horseshoes, directly intersecting with their own preimages. Our global analysis suggests that the structure of the classical Chua attractor and other figure-eight attractors might be more complex than previously thought.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-10T06:28:43Z
DOI: 10.1063/5.0139064
-
- Mitigation of limit cycle oscillations in a turbulent thermoacoustic
system via delayed acoustic self-feedback-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Ankit Sahay, Abhishek Kushwaha, Samadhan A. Pawar, Midhun P. R., Jayesh M. Dhadphale, R. I. Sujith
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
We report the occurrence of amplitude death (AD) of limit cycle oscillations in a bluff body stabilized turbulent combustor through delayed acoustic self-feedback. Such feedback control is achieved by coupling the acoustic field of the combustor to itself through a single coupling tube attached near the anti-node position of the acoustic standing wave. We observe that the amplitude and dominant frequency of the limit cycle oscillations gradually decrease as the length of the coupling tube is increased. Complete suppression (AD) of these oscillations is observed when the length of the coupling tube is nearly [math] times the wavelength of the fundamental acoustic mode of the combustor. Meanwhile, as we approach this state of amplitude death, the dynamical behavior of acoustic pressure changes from the state of limit cycle oscillations to low-amplitude chaotic oscillations via intermittency. We also study the change in the nature of the coupling between the unsteady flame dynamics and the acoustic field as the length of the coupling tube is increased. We find that the temporal synchrony between these oscillations changes from the state of synchronized periodicity to desynchronized aperiodicity through intermittent synchronization. Furthermore, we reveal that the application of delayed acoustic self-feedback with optimum feedback parameters completely disrupts the positive feedback loop between hydrodynamic, acoustic, and heat release rate fluctuations present in the combustor during thermoacoustic instability, thus mitigating instability. We anticipate this method to be a viable and cost-effective option to mitigate thermoacoustic oscillations in turbulent combustion systems used in practical propulsion and power systems.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-10T06:28:38Z
DOI: 10.1063/5.0129512
-
- Erratum: “Controlling species densities in structurally perturbed
intransitive cycles with higher-order interactions” [Chaos 32(10),
103122 (2022)]-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Sourin Chatterjee, Sayantan Nag Chowdhury, Dibakar Ghosh, Chittaranjan Hens
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-10T06:28:34Z
DOI: 10.1063/5.0150932
-
- Observers-based event-triggered adaptive fuzzy backstepping
synchronization of uncertain fractional order chaotic systems-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Hanlin Dong, Jinde Cao, Heng Liu
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
In this paper, for a class of uncertain fractional order chaotic systems with disturbances and partially unmeasurable states, an observer-based event-triggered adaptive fuzzy backstepping synchronization control method is proposed. Fuzzy logic systems are employed to estimate unknown functions in the backstepping procedure. To avoid the explosion of the complexity problem, a fractional order command filter is designed. Simultaneously, in order to reduce the filter error and improve the synchronization accuracy, an effective error compensation mechanism is devised. In particular, a disturbance observer is devised in the case of unmeasurable states, and a state observer is established to estimate the synchronization error of the master–slave system. The designed controller can ensure that the synchronization error converges to a small neighborhood around the origin finally and all signals are semiglobal uniformly ultimately bounded, and meanwhile, it is conducive to avoiding Zeno behavior. Finally, two numerical simulations are given to verify the effectiveness and accuracy of the proposed scheme.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-05T08:21:35Z
DOI: 10.1063/5.0135758
-
- The impact of nodes of information dissemination on epidemic spreading in
dynamic multiplex networks-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Minyu Feng, Xiangxi Li, Yuhan Li, Qin Li
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
Epidemic spreading processes on dynamic multiplex networks provide a more accurate description of natural spreading processes than those on single layered networks. To describe the influence of different individuals in the awareness layer on epidemic spreading, we propose a two-layer network-based epidemic spreading model, including some individuals who neglect the epidemic, and we explore how individuals with different properties in the awareness layer will affect the spread of epidemics. The two-layer network model is divided into an information transmission layer and a disease spreading layer. Each node in the layer represents an individual with different connections in different layers. Individuals with awareness will be infected with a lower probability compared to unaware individuals, which corresponds to the various epidemic prevention measures in real life. We adopt the micro-Markov chain approach to analytically derive the threshold for the proposed epidemic model, which demonstrates that the awareness layer affects the threshold of disease spreading. We then explore how individuals with different properties would affect the disease spreading process through extensive Monte Carlo numerical simulations. We find that individuals with high centrality in the awareness layer would significantly inhibit the transmission of infectious diseases. Additionally, we propose conjectures and explanations for the approximately linear effect of individuals with low centrality in the awareness layer on the number of infected individuals.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-05T08:20:35Z
DOI: 10.1063/5.0142386
-
- Sex, ducks, and rock “n” roll: Mathematical model of sexual
response-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: K. B. Blyuss, Y. N. Kyrychko
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
In this paper, we derive and analyze a mathematical model of a sexual response. As a starting point, we discuss two studies that proposed a connection between a sexual response cycle and a cusp catastrophe and explain why that connection is incorrect but suggests an analogy with excitable systems. This then serves as a basis for derivation of a phenomenological mathematical model of a sexual response, in which the variables represent levels of physiological and psychological arousal. Bifurcation analysis is performed to identify stability properties of the model’s steady state, and numerical simulations are performed to illustrate different types of behavior that can be observed in the model. Solutions corresponding to the dynamics associated with the Masters–Johnson sexual response cycle are represented by “canard”-like trajectories that follow an unstable slow manifold before making a large excursion in the phase space. We also consider a stochastic version of the model, for which spectrum, variance, and coherence of stochastic oscillations around a deterministically stable steady state are found analytically, and confidence regions are computed. Large deviation theory is used to explore the possibility of stochastic escape from the neighborhood of the deterministically stable steady state, and the methods of an action plot and quasi-potential are employed to compute most probable escape paths. We discuss implications of the results for facilitating better quantitative understanding of the dynamics of a human sexual response and for improving clinical practice.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-04T06:56:49Z
DOI: 10.1063/5.0143190
-
- Solving the non-local Fokker–Planck equations by deep learning
-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Senbao Jiang, Xiaofan Li
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
Physics-informed neural networks (PiNNs) recently emerged as a powerful solver for a large class of partial differential equations (PDEs) under various initial and boundary conditions. In this paper, we propose trapz-PiNNs, physics-informed neural networks incorporated with a modified trapezoidal rule recently developed for accurately evaluating fractional Laplacian and solve the space-fractional Fokker–Planck equations in 2D and 3D. We describe the modified trapezoidal rule in detail and verify the second-order accuracy. We demonstrate that trapz-PiNNs have high expressive power through predicting the solution with low [math] relative error by a variety of numerical examples. We also use local metrics, such as point-wise absolute and relative errors, to analyze where it could be further improved. We present an effective method for improving the performance of trapz-PiNN on local metrics, provided that physical observations or high-fidelity simulation of the true solution are available. The trapz-PiNN is able to solve PDEs with fractional Laplacian with arbitrary [math] and on rectangular domains. It also has the potential to be generalized into higher dimensions or other bounded domains.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-03T04:11:16Z
DOI: 10.1063/5.0128935
-
- Lyapunov exponents of multi-state cellular automata
-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: M. Vispoel, A. J. Daly, J. M. Baetens
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
In order to describe the sensitivity of a cellular automaton (CA) to a small change in its initial configuration, one can attempt to extend the notion of Lyapunov exponents as defined for continuous dynamical systems to a CA. So far, such attempts have been limited to a CA with two states. This poses a significant limitation on their applicability, as many CA-based models rely on three or more states. In this paper, we generalize the existing approach to an arbitrary [math]-dimensional [math]-state CA with either a deterministic or probabilistic update rule. Our proposed extension establishes a distinction between different kinds of defects that can propagate, as well as the direction in which they propagate. Furthermore, in order to arrive at a comprehensive insight into CA’s stability, we introduce additional concepts, such as the average Lyapunov exponent and the correlation coefficient of the difference pattern growth. We illustrate our approach for some interesting three-state and four-state rules, as well as a CA-based forest-fire model. In addition to making the existing methods generally applicable, our extension makes it possible to identify some behavioral features that allow us to distinguish a Class IV CA from a Class III CA (according to Wolfram’s classification), which has been proven to be difficult.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-03T04:11:15Z
DOI: 10.1063/5.0139849
-
- Detecting hidden nodes in networks based on random variable resetting
method-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Weinuo Jiang, Shihong Wang
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
Reconstructing network connections from measurable data facilitates our understanding of the mechanism of interactions between nodes. However, the unmeasurable nodes in real networks, also known as hidden nodes, introduce new challenges for reconstruction. There have been some hidden node detection methods, but most of them are limited by system models, network structures, and other conditions. In this paper, we propose a general theoretical method for detecting hidden nodes based on the random variable resetting method. We construct a new time series containing hidden node information based on the reconstruction results of random variable resetting, theoretically analyze the autocovariance of the time series, and finally provide a quantitative criterion for detecting hidden nodes. We numerically simulate our method in discrete and continuous systems and analyze the influence of main factors. The simulation results validate our theoretical derivation and illustrate the robustness of the detection method under different conditions.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-03T04:11:14Z
DOI: 10.1063/5.0134953
-
- Topological-numerical analysis of a two-dimensional discrete neuron model
-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Paweł Pilarczyk, Justyna Signerska-Rynkowska, Grzegorz Graff
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
We conduct computer-assisted analysis of a two-dimensional model of a neuron introduced by Chialvo in 1995 [Chaos, Solitons Fractals 5, 461–479]. We apply the method of rigorous analysis of global dynamics based on a set-oriented topological approach, introduced by Arai et al. in 2009 [SIAM J. Appl. Dyn. Syst. 8, 757–789] and improved and expanded afterward. Additionally, we introduce a new algorithm to analyze the return times inside a chain recurrent set. Based on this analysis, together with the information on the size of the chain recurrent set, we develop a new method that allows one to determine subsets of parameters for which chaotic dynamics may appear. This approach can be applied to a variety of dynamical systems, and we discuss some of its practical aspects.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-03T04:11:14Z
DOI: 10.1063/5.0129859
-
- Chaotic dynamics of the Hénon map and neuronal input–output: A
comparison with neurophysiological data-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Natalí Guisande, Monserrat Pallares di Nunzio, Nataniel Martinez, Osvaldo A. Rosso, Fernando Montani
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
In this study, the Hénon map was analyzed using quantifiers from information theory in order to compare its dynamics to experimental data from brain regions known to exhibit chaotic behavior. The goal was to investigate the potential of the Hénon map as a model for replicating chaotic brain dynamics in the treatment of Parkinson’s and epilepsy patients. The dynamic properties of the Hénon map were compared with data from the subthalamic nucleus, the medial frontal cortex, and a [math]-DG model of neuronal input–output with easy numerical implementation to simulate the local behavior of a population. Using information theory tools, Shannon entropy, statistical complexity, and Fisher’s information were analyzed, taking into account the causality of the time series. For this purpose, different windows over the time series were considered. The findings revealed that neither the Hénon map nor the [math]-DG model could perfectly replicate the dynamics of the brain regions studied. However, with careful consideration of the parameters, scales, and sampling used, they were able to model some characteristics of neural activity. According to these results, normal neural dynamics in the subthalamic nucleus region may present a more complex spectrum within the complexity–entropy causality plane that cannot be represented by chaotic models alone. The dynamic behavior observed in these systems using these tools is highly dependent on the studied temporal scale. As the size of the sample studied increases, the dynamics of the Hénon map become increasingly different from those of biological and artificial neural systems.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-03T04:11:13Z
DOI: 10.1063/5.0142773
-
- Propagating wave merging in a precipitation reaction
-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Boshir Ahmed, David Mersing, Mark R. Tinsley, Kenneth Showalter
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
Propagating precipitation waves are a remarkable form of spatiotemporal behavior that arise through the coupling of reaction, diffusion, and precipitation. We study a system with a sodium hydroxide outer electrolyte and an aluminum hydroxide inner electrolyte. In a redissolution Liesegang system, a single propagating precipitation band moves down through the gel, with precipitate formed at the band front and precipitate dissolved at the band back. Complex spatiotemporal waves occur within the propagating precipitation band, including counter-rotating spiral waves, target patterns, and annihilation of waves on collision. We have also carried out experiments in thin slices of gel, which have revealed propagating waves of a diagonal precipitation feature within the primary precipitation band. These waves display a wave merging phenomenon in which two horizontally propagating waves merge into a single wave. Computational modeling permits the development of a detailed understanding of the complex dynamical behavior.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-03T03:58:59Z
DOI: 10.1063/5.0139698
-
- Mean-field model of synchronization for open-loop, swirl controlled
thermoacoustic system-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Samarjeet Singh, Ankit Kumar Dutta, Jayesh M. Dhadphale, Amitesh Roy, R. I. Sujith, Swetaprovo Chaudhuri
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
Open-loop control is known to be an effective strategy for controlling self-excited periodic oscillations, known as thermoacoustic instability, in turbulent combustors. Here, we present experimental observations and a synchronization model for the suppression of thermoacoustic instability achieved by rotating the otherwise static swirler in a lab-scale turbulent combustor. Starting with the state of thermoacoustic instability in the combustor, we find that a progressive increase in the swirler rotation rate leads to a transition from the state of limit cycle oscillations to the low-amplitude aperiodic oscillations through a state of intermittency. To model such a transition while also quantifying the underlying synchronization characteristics, we extend the model of Dutta et al. [Phys. Rev. E 99, 032215 (2019)] by introducing a feedback between the ensemble of phase oscillators and the acoustic. The coupling strength in the model is determined by considering the effect of the acoustic and swirl frequencies. The link between the model and experimental results is quantitatively established by implementing an optimization algorithm for model parameter estimation. We show that the model is capable of replicating the bifurcation characteristics, nonlinear features of time series, probability density function, and amplitude spectrum of acoustic pressure and heat release rate fluctuations at various dynamical states observed during the transition to the state of suppression. Most importantly, we discuss the flame dynamics and demonstrate that the model without any spatial inputs qualitatively captures the characteristics of the spatiotemporal synchronization between the local heat release rate fluctuations and the acoustic pressure that underpins a transition to the state of suppression. As a result, the model emerges as a powerful tool for explaining and controlling instabilities in thermoacoustic and other extended fluid dynamical systems, where spatiotemporal interactions lead to rich dynamical phenomena.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-03T03:58:57Z
DOI: 10.1063/5.0136385
-
- Dynamical analysis of monkeypox transmission incorporating optimal
vaccination and treatment with cost-effectiveness-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Suvankar Majee, Soovoojeet Jana, T. K. Kar
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
The ongoing monkeypox outbreak that began in the UK has currently spread to every continent. Here, we use ordinary differential equations to build a nine-compartmental mathematical model to examine the dynamics of monkeypox transmission. The basic reproduction number for both humans ([math]) and animals ([math]) is obtained using the next-generation matrix technique. Depending on the values of [math] and [math], we discovered that there are three equilibria. The current study also looks at the stability of all equilibria. We discovered that the model experiences transcritical bifurcation at [math] for any value of [math] and at [math] for [math]. This is the first study that, to the best of our knowledge, has constructed and solved an optimal monkeypox control strategy while taking vaccination and treatment controls into consideration. The infected averted ratio and incremental cost-effectiveness ratio were calculated to evaluate the cost-effectiveness of all viable control methods. Using the sensitivity index technique, the parameters used in the formulation of [math] and [math] are scaled.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-03T03:58:56Z
DOI: 10.1063/5.0139157
-
- Koopman analysis of the periodic Korteweg–de Vries equation
-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Jeremy P. Parker, Claire Valva
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
The eigenspectrum of the Koopman operator enables the decomposition of nonlinear dynamics into a sum of nonlinear functions of the state space with purely exponential and sinusoidal time dependence. For a limited number of dynamical systems, it is possible to find these Koopman eigenfunctions exactly and analytically. Here, this is done for the Korteweg–de Vries equation on a periodic interval using the periodic inverse scattering transform and some concepts of algebraic geometry. To the authors’ knowledge, this is the first complete Koopman analysis of a partial differential equation, which does not have a trivial global attractor. The results are shown to match the frequencies computed by the data-driven method of dynamic mode decomposition (DMD). We demonstrate that in general, DMD gives a large number of eigenvalues near the imaginary axis and show how these should be interpreted in this setting.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-03T03:58:55Z
DOI: 10.1063/5.0137088
-
- Interpretable polynomial neural ordinary differential equations
-
Free pre-print version: Loading...Rate this result: What is this?Please help us test our new pre-print finding feature by giving the pre-print link a rating.
A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Authors: Colby Fronk, Linda Petzold
Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 4, April 2023.
Neural networks have the ability to serve as universal function approximators, but they are not interpretable and do not generalize well outside of their training region. Both of these issues are problematic when trying to apply standard neural ordinary differential equations (ODEs) to dynamical systems. We introduce the polynomial neural ODE, which is a deep polynomial neural network inside of the neural ODE framework. We demonstrate the capability of polynomial neural ODEs to predict outside of the training region, as well as to perform direct symbolic regression without using additional tools such as SINDy.
Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science
PubDate: 2023-04-03T03:58:54Z
DOI: 10.1063/5.0130803
-
