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Authors:Stefan Awender, Renate Wackerbauer, Greg A. Breed Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. The complexity of real food webs involves uncertainty in data and in underlying ecological processes, and modeling approaches deal with these challenges differently. Generalized modeling provides a linear stability analysis without narrow specification of all processes, and conventional dynamical systems models approximate functional forms to discuss trajectories in phase space. This study compares results and ecological interpretations from both methods in four-species ecological networks at steady state. We find that a specific (dynamical systems) model only provides a subset of stability data from the generalized model, which spans many plausible dynamic scenarios, allowing for conflicting results. Nevertheless, both approaches reveal that fixed points become stable when nutrient flows to predators are fettered and even more when the basal growth rate approaches a maximum. The specific model identifies a distinct ecosystem response to bottom-up forcing, the enrichment of lower trophic levels. Enrichment stabilizes a fixed point when basal species are in a resource-deprived environment but destabilizes it if resources become more abundant. The generalized model provides less specific information since infinitely many paths of enrichment are hypothetical. Nevertheless, generalized modeling of ecological systems is a powerful technique that enables a meta analysis of these uncertain complex systems. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-17T03:59:57Z DOI: 10.1063/5.0131352
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Authors:Elaheh Sayari, Enrique C. Gabrick, Fernando S. Borges, Fátima E. Cruziniani, Paulo R. Protachevicz, Kelly C. Iarosz, José D. Szezech, Antonio M. Batista Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. Cognitive tasks in the human brain are performed by various cortical areas located in the cerebral cortex. The cerebral cortex is separated into different areas in the right and left hemispheres. We consider one human cerebral cortex according to a network composed of coupled subnetworks with small-world properties. We study the burst synchronization and desynchronization in a human neuronal network under external periodic and random pulsed currents. With and without external perturbations, the emergence of bursting synchronization is observed. Synchronization can contribute to the processing of information, however, there are evidences that it can be related to some neurological disorders. Our results show that synchronous behavior can be suppressed by means of external pulsed currents. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-17T03:59:57Z DOI: 10.1063/5.0135399
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Authors:Fahad Al Saadi, Pedro Parra-Rivas Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. Spatially extended patterns and multistability of possible different states are common in many ecosystems, and their combination has an important impact on their dynamical behaviors. One potential combination involves tristability between a patterned state and two different uniform states. Using a simplified version of the Gilad–Meron model for dryland ecosystems, we study the organization, in bifurcation terms, of the localized structures arising in tristable regimes. These states are generally related to the concept of wave front locking and appear in the form of spots and gaps of vegetation. We find that the coexistence of localized spots and gaps, within tristable configurations, yields the appearance of hybrid states. We also study the emergence of spatiotemporal localized states consisting of a portion of a periodic pattern embedded in a uniform Hopf-like oscillatory background in a subcritical Turing–Hopf dynamical regime. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-17T03:59:56Z DOI: 10.1063/5.0133576
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Authors:Chiara Barà, Laura Sparacino, Riccardo Pernice, Yuri Antonacci, Alberto Porta, Dimitris Kugiumtzis, Luca Faes Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. This work presents a comparison between different approaches for the model-free estimation of information-theoretic measures of the dynamic coupling between short realizations of random processes. The measures considered are the mutual information rate (MIR) between two random processes [math] and [math] and the terms of its decomposition evidencing either the individual entropy rates of [math] and [math] and their joint entropy rate, or the transfer entropies from [math] to [math] and from [math] to [math] and the instantaneous information shared by [math] and [math]. All measures are estimated through discretization of the random variables forming the processes, performed either via uniform quantization (binning approach) or rank ordering (permutation approach). The binning and permutation approaches are compared on simulations of two coupled non-identical Hènon systems and on three datasets, including short realizations of cardiorespiratory (CR, heart period and respiration flow), cardiovascular (CV, heart period and systolic arterial pressure), and cerebrovascular (CB, mean arterial pressure and cerebral blood flow velocity) measured in different physiological conditions, i.e., spontaneous vs paced breathing or supine vs upright positions. Our results show that, with careful selection of the estimation parameters (i.e., the embedding dimension and the number of quantization levels for the binning approach), meaningful patterns of the MIR and of its components can be achieved in the analyzed systems. On physiological time series, we found that paced breathing at slow breathing rates induces less complex and more coupled CR dynamics, while postural stress leads to unbalancing of CV interactions with prevalent baroreflex coupling and to less complex pressure dynamics with preserved CB interactions. These results are better highlighted by the permutation approach, thanks to its more parsimonious representation of the discretized dynamic patterns, which allows one to explore interactions with longer memory while limiting the curse of dimensionality. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-16T04:02:17Z DOI: 10.1063/5.0140641
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Authors:Peican Zhu, Zhaoheng Cao, Chen Liu, Chen Chu, Zhen Wang Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. Cooperation is a widespread phenomenon in human society and plays a significant role in achieving synchronization of various systems. However, there has been limited progress in studying the co-evolution of synchronization and cooperation. In this manuscript, we investigate how reinforcement learning affects the evolution of synchronization and cooperation. Namely, the payoff of an agent depends not only on the cooperation dynamic but also on the synchronization dynamic. Agents have the option to either cooperate or defect. While cooperation promotes synchronization among agents, defection does not. We report that the dynamic feature, which indicates the action switching frequency of the agent during interactions, promotes synchronization. We also find that cooperation and synchronization are mutually reinforcing. Furthermore, we thoroughly analyze the potential reasons for synchronization promotion due to the dynamic feature from both macro- and microperspectives. Additionally, we conduct experiments to illustrate the differences in the synchronization-promoting effects of cooperation and dynamic features. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-16T04:01:26Z DOI: 10.1063/5.0141824
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Authors:Rui Ma, Yayao Zhang, Ziqian Yang, Jürgen Kurths, Meng Zhan, Congping Lin Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. Synchronization stability is one of central problems in power systems, and it is becoming much more complicated with the high penetration of renewable energy and power electronics devices. In this paper, we review recent work by several nonlinear models for renewable-dominated power systems in terms of multiple timescales, in particular, grid-tied converters within the DC voltage timescale. For the simplest model, a second-order differential equations called the generalized swing equation by considering only the phase-locked loop (PLL) is obtained, which shows a similar form with the well-known swing equation for a synchronous generator in the traditional power systems. With more outer controllers included, fourth-order and fifth-order models can be obtained. The fourth-order model is called the extended generalized swing equation, exhibiting the combined function of grid synchronization and active power balance on the DC capacitor. In addition, a nonlinear model for a two coupled converter system is given. Based on these studies, we find that the PLL plays a key role in synchronization stability. In summary, the value of this paper is to clarify the key concept of the synchronization stability in renewable-dominated power systems based on different nonlinear models, which still lacks systematic studies and is controversial in the field of electrical power engineering. Meanwhile, it clearly uncovers that the synchronization stability of converters has its root in the phase synchronization concept in nonlinear sciences. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-16T04:01:17Z DOI: 10.1063/5.0136975
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Authors:Luis A. Martinez-Vaquero Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. This work studies the impact of economic inequality on the evolution of intolerance through a reputation-based model of indirect reciprocity. Results show that economic inequality is a powerful enhancer of intolerance, inducing the escalation of out-group discrimination even without the presence of new intolerant mutants. It also generates behavior modifications within tolerant disfavored minorities: their members either relax punishments against the uncooperative or prioritize helping the wealthy, even suffering discrimination in return. On the other hand, the redistribution of wealth is proven as a viable solution to avoid the spread of intolerance as long as it increases equality and is implemented before intolerance permeates part of the population. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-14T02:45:21Z DOI: 10.1063/5.0135376
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Authors:Jussara Dias, Arthur N. Montanari, Elbert E. N. Macau Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. Interconnected systems with critical infrastructures can be affected by small failures that may trigger a large-scale cascade of failures, such as blackouts in power grids. Vulnerability indices provide quantitative measures of a network resilience to component failures, assessing the break of information or energy flow in a system. Here, we focus on a network vulnerability analysis, that is, indices based solely on the network structure and its static characteristics, which are reliably available for most complex networks. This work studies the structural connectivity of power grids, assessing the main centrality measures in network science to identify vulnerable components (transmission lines or edges) to attacks and failures. Specifically, we consider centrality measures that implicitly model the power flow distribution in power systems. This framework allow us to show that the efficiency of the power flow in a grid can be highly sensitive to attacks on specific (central) edges. Numerical results are presented for randomly generated power-grid models and established power-grid benchmarks, where we demonstrate that the system’s energy efficiency is more vulnerable to attacks on edges that are central to the power flow distribution. We expect that the vulnerability indices investigated in our work can be used to guide the design of structurally resilient power grids. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-14T02:25:16Z DOI: 10.1063/5.0137919
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Authors:Neeraj Chaubey, Pankaj Kumar Shaw, S. Mukherjee, A. Sen Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. We report the first experimental observations of phase switching in a system of three coupled plasma sources. Two of the plasma sources are inductively coupled to each other while the third one is directly coupled to one of them. The coupled system acquires a frequency pulling synchronized state following which a transition occurs to a frequency entrainment state with an increase in the frequency of the directly coupled system. We also observe a sudden jump from a lower to a higher frequency entrainment state and a concomitant phase switching between the oscillations of the two directly coupled sources while the phase difference between the inductively coupled sources remains constant. These experimental findings are established using various diagnostic tools, such as the Fourier spectra, frequency bifurcation plots, Lissajous plots, and Hilbert transforms of the data. The experimental results are qualitatively modeled using three coupled van der Pol equations, in which two of them are environmentally coupled while the third one is directly coupled with one of them. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-14T02:25:11Z DOI: 10.1063/5.0130226
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Authors:David Sánchez, Luciano Zunino, Juan De Gregorio, Raúl Toral, Claudio Mirasso Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. Words are fundamental linguistic units that connect thoughts and things through meaning. However, words do not appear independently in a text sequence. The existence of syntactic rules induces correlations among neighboring words. Using an ordinal pattern approach, we present an analysis of lexical statistical connections for 11 major languages. We find that the diverse manners that languages utilize to express word relations give rise to unique pattern structural distributions. Furthermore, fluctuations of these pattern distributions for a given language can allow us to determine both the historical period when the text was written and its author. Taken together, our results emphasize the relevance of ordinal time series analysis in linguistic typology, historical linguistics, and stylometry. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-14T02:25:08Z DOI: 10.1063/5.0139852
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Authors:Christoph Bandt Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. Order patterns apply well to many fields, because of minimal stationarity assumptions. Here, we fix the methodology of patterns of length 3 by introducing an orthogonal system of four pattern contrasts, that is, weighted differences of pattern frequencies. These contrasts are statistically independent and turn up as eigenvectors of a covariance matrix both in the independence model and the random walk model. The most important contrast is the turning rate. It can be used to evaluate sleep depth directly from EEG (electroencephalographic brain data). The paper discusses fluctuations of permutation entropy, statistical tests, and the need of new models for noises like EEG. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-14T02:25:08Z DOI: 10.1063/5.0132602
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Authors:Hao Chen, Lin Wang, Xiaofan Wang Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. Inter-network combat and intra-network cooperation among structured systems are likely to have been recurrent features of human evolutionary history; however, little research has investigated the combat mechanism between structured systems that the adversarial interactions will cause the disability of agents and agents are prone to seek cooperation with neighbors. Hence, the current study has proposed a two-network combat game model and designed the corresponding rules of how to attack, how to be disabled, how to cooperate, and how to win. First, within the framework of our model, we have simulated the combat among four common network structures—the Erdős–Rényi (ER) random network, the grid graph, the small-world network, and the scale-free network. We found that the grid network always holds the highest winning percentage, while the ER random graph is most likely to lose when combating with the other three network structures. For each structure, we have also simulated the combat between the same network structures with different generating parameters. The simulations reveal that the small-world property and heterogeneity can promote winning a combat. Besides, by broadening and deepening cooperation, we have found that broader cooperation helps defeat the opposite system on grid and scale-free networks, yet hinders it on ER and Watts–Strogatz (WS) networks, while deeper cooperation can benefit to winning except on scale-free networks. These findings inform our understanding of the effects of structure and cooperation in a combat. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-14T02:25:07Z DOI: 10.1063/5.0137338
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Authors:Paolo Bartesaghi Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. Synchronization and resonance on networks are some of the most remarkable collective dynamical phenomena. The network topology, or the nature and distribution of the connections within an ensemble of coupled oscillators, plays a crucial role in shaping the local and global evolution of the two phenomena. This article further explores this relationship within a compact mathematical framework and provides new contributions on certain pivotal issues, including a closed bound for the average synchronization time in arbitrary topologies; new evidences of the effect of the coupling strength on this time; exact closed expressions for the resonance frequencies in terms of the eigenvalues of the Laplacian matrix; a measure of the effectiveness of an influencer node’s impact on the network; and, finally, a discussion on the existence of a resonant synchronized state. Some properties of the solution of the linear swing equation are also discussed within the same setting. Numerical experiments conducted on two distinct real networks—a social network and a power grid—illustrate the significance of these results and shed light on intriguing aspects of how these processes can be interpreted within networks of this kind. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-14T02:25:05Z DOI: 10.1063/5.0134285
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Authors:D. Vignesh, Santo Banerjee Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. Chemical reactions form the basis of life and understanding the different patterns and unpredictable changes in the reactions are noteworthy in real life situations. The article aims at constructing a mathematical model of two step reversible chemical reactions with a Caputo fractional difference operator. The reversible reaction involves the breakdown of an ester compound in the presence of water followed by the formation of fatty acid salts from the reaction of a free fatty acid with alkali hydroxide, such as NaOH. Using bifurcation diagrams, the chaotic response exhibited by the system is illustrated for state variables with identical fractional order and variables with non-identical fractional orders. The changes in periodic states of the system are investigated for each state variables with time varying plots and maximum Lyapunov exponents using the Jacobian matrix method are presented in support of the bifurcation diagrams. The synchronization of the subsystems of the proposed system is achieved with nonlinear control functions. Numerical simulations are presented to provide comparison of commensurate and incommensurate order models. Understanding the nature of these processes has significant applications in the production of bio-fuels from vegetable oils and animal fats by a transesterification reaction. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-14T02:25:01Z DOI: 10.1063/5.0139967
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Authors:Lucille Calmon, Sanjukta Krishnagopal, Ginestra Bianconi Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. We propose Local Dirac Synchronization that uses the Dirac operator to capture the dynamics of coupled nodes and link signals on an arbitrary network. In Local Dirac Synchronization, the harmonic modes of the dynamics oscillate freely while the other modes are interacting non-linearly, leading to a collectively synchronized state when the coupling constant of the model is increased. Local Dirac Synchronization is characterized by discontinuous transitions and the emergence of a rhythmic coherent phase. In this rhythmic phase, one of the two complex order parameters oscillates in the complex plane at a slow frequency (called emergent frequency) in the frame in which the intrinsic frequencies have zero average. Our theoretical results obtained within the annealed approximation are validated by extensive numerical results on fully connected networks and sparse Poisson and scale-free networks. Local Dirac Synchronization on both random and real networks, such as the connectome of Caenorhabditis Elegans, reveals the interplay between topology (Betti numbers and harmonic modes) and non-linear dynamics. This unveils how topology might play a role in the onset of brain rhythms. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-13T06:23:35Z DOI: 10.1063/5.0132468
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Authors:M. Herein, T. Tél, T. Haszpra Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. We review the recent results of large ensemble climate projections considering them to be the simulations of chaotic systems. The quick spread of an initially localized ensemble in the first weeks after initialization is an appearance of the butterfly effect, illustrating the unpredictability of the dynamics. We show that the growth rate of uncertainty (an analog of the Lyapunov exponent) can be determined right after initialization. The next phase corresponds to a convergence of the no longer localized ensemble to the time-dependent climate attractor and requires a much longer time. After convergence takes place, the ensemble faithfully represents the climate dynamics. Concerning a credible simulation, the observed signal should then wander within the spread of the converged ensemble all the time, i.e., to behave just as any of the ensemble members. As a manifestation of the chaotic-like climate dynamics, one can imagine that beyond the single, observed time-dependent climate, a plethora of parallel climate realizations exists. Converged climate ensembles also define the probability distribution by which the physical quantities of the different climate realizations occur. Large ensemble simulations were shown earlier to be credible in the sense formulated. Here, in addition, an extended credibility condition is given, which requires the ensemble to be a converged ensemble, valid also for low-dimensional models. Interestingly, to the best of our knowledge, no low-order physical or engineering systems subjected to time-dependent forcings are known for which a comparison between simulation and experiment would be available. As illustrative examples, the CESM1-LE climate model and a chaotic pendulum are taken. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-13T06:23:34Z DOI: 10.1063/5.0136719
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Authors:Manfred Denker Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. It is shown by Denker and Yuri [Contemp. Math. 63, 93–108 (2015)] that “general” iterated function systems admit conformal families of measures. Here, we relate this property to estimating Hausdorff dimension in the expanding case, including overlaps. A correct formulation of Theorem 3.11 in the above paper is provided as well. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-13T06:23:34Z DOI: 10.1063/5.0136663
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Authors:Shreenivas Rangarajan, Dheeraj Tripathi, J. Venkatramani Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. The non-normal nature and transient growth in amplitude and energy of a pitch-plunge aeroelastic system undergoing dynamic stall are explored in this paper through numerical and supporting experimental studies. Wind tunnel experiments, carried out for a canonical pitch-plunge aeroelastic system in a subsonic wind tunnel, show that the system undergoes stall flutter instability via a sub-critical Hopf bifurcation. The aeroelastic responses indicate a transient growth in amplitude and energy—possibly triggering the sub-criticality, which is critical from the purview of structural safety. The system also shows transient energy growth followed by decaying oscillation for certain initial conditions, whereas sustained limit cycle oscillations are encountered for other initial conditions at flow speeds lower than the critical speed. The triggering behavior observed in the wind tunnel experiments is understood better by resorting to study the numerical model of the nonlinear aeroelastic system. To that end, a modified semi-empirical Leishman–Beddoes dynamic stall model is adopted to represent the nonlinear aerodynamic loads of the pitch-plunge aeroelastic system. The underlying linear operator and its pseudospectral analysis indicate that the aeroelastic system is non-normal, causing amplification in amplitude and energy for a short period. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-13T06:23:32Z DOI: 10.1063/5.0143321
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Authors:Sabina Adhikari, Juan G. Restrepo, Per Sebastian Skardal Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. We study the effect of structured higher-order interactions on the collective behavior of coupled phase oscillators. By combining a hypergraph generative model with dimensionality reduction techniques, we obtain a reduced system of differential equations for the system’s order parameters. We illustrate our framework with the example of a hypergraph with hyperedges of sizes 2 (links) and 3 (triangles). For this case, we obtain a set of two coupled nonlinear algebraic equations for the order parameters. For strong values of coupling via triangles, the system exhibits bistability and explosive synchronization transitions. We find conditions that lead to bistability in terms of hypergraph properties and validate our predictions with numerical simulations. Our results provide a general framework to study the synchronization of phase oscillators in hypergraphs, and they can be extended to hypergraphs with hyperedges of arbitrary sizes, dynamic-structural correlations, and other features. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-09T05:12:41Z DOI: 10.1063/5.0116747
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Authors:Yasen Wang, Cheng Cheng, Hongwei Sun, Junyang Jin, Huazhen Fang Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. The identification of diffusion processes is challenging for many real-world systems with sparsely sampled observation data. In this work, we propose a data augmentation-based sparse Bayesian learning method to identify a class of diffusion processes from sparsely sampled data. We impute latent unsampled diffusion paths between adjacent observations and construct a candidate model for the diffusion processes with the sparsity-inducing prior on model parameters. Given the augmented data and candidate model, we investigate the full joint posterior distribution of all the parameters and latent diffusion paths under a Bayesian learning framework. We then design a Markov chain Monte Carlo sampler with non-degenerate acceptance probability on system dimension to draw samples from the posterior distribution to estimate the parameters and latent diffusion paths. Particularly, the proposed method can handle sparse data that are regularly or irregularly sampled in time. Simulations on the well-known Langevin equation, homogeneous diffusion in a symmetric double-well potential, and stochastic Lotka–Volterra equation demonstrate the effectiveness and considerable accuracy of the proposed method. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-08T07:06:39Z DOI: 10.1063/5.0124763
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Authors:Ling-Wei Kong, Yang Weng, Bryan Glaz, Mulugeta Haile, Ying-Cheng Lai Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. We articulate the design imperatives for machine learning based digital twins for nonlinear dynamical systems, which can be used to monitor the “health” of the system and anticipate future collapse. The fundamental requirement for digital twins of nonlinear dynamical systems is dynamical evolution: the digital twin must be able to evolve its dynamical state at the present time to the next time step without further state input—a requirement that reservoir computing naturally meets. We conduct extensive tests using prototypical systems from optics, ecology, and climate, where the respective specific examples are a chaotic [math] laser system, a model of phytoplankton subject to seasonality, and the Lorenz-96 climate network. We demonstrate that, with a single or parallel reservoir computer, the digital twins are capable of a variety of challenging forecasting and monitoring tasks. Our digital twin has the following capabilities: (1) extrapolating the dynamics of the target system to predict how it may respond to a changing dynamical environment, e.g., a driving signal that it has never experienced before, (2) making continual forecasting and monitoring with sparse real-time updates under non-stationary external driving, (3) inferring hidden variables in the target system and accurately reproducing/predicting their dynamical evolution, (4) adapting to external driving of different waveform, and (5) extrapolating the global bifurcation behaviors to network systems of different sizes. These features make our digital twins appealing in applications, such as monitoring the health of critical systems and forecasting their potential collapse induced by environmental changes or perturbations. Such systems can be an infrastructure, an ecosystem, or a regional climate system. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-07T07:23:07Z DOI: 10.1063/5.0138661
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Authors:Ratnesh K. Pandey, Ram Pratap Yadav, Tanuj Kumar, Ashish Kumar, Sachin Pathak, Shikha Awasthi, Udai B. Singh, Avinash C. Pandey Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. We present the morphological evolution and fractal characterizations of CaF2 thin-film surfaces modified by bombardment with 100 MeV Au+8 ions at various fluences. Atomic force microscopy (AFM) combined with line profile and two-dimensional power spectral density (2D-PSD) analysis was utilized to investigate the evolution of surface morphology as a function of fluence. The AFM images were utilized to investigate the relationship between fractal dimension, roughness exponent, lateral correlation length, and ion fluence. The surface erosion owing to sputtering was depicted using Rutherford backscattering spectrometry. The structural characteristics' dependency on fluence was explored with the help of glancing angle x-ray diffraction measurements on virgin and irradiated samples. Tensile stress calculated using a peak shift in the glancing angle x-ray diffractogram showed an increase in tensile stress with fluence that caused the surface to crack after the fracture strength of the surface was crossed. 2D-PSD analysis signified the role of sputtering over surface diffusion for the observed surface modifications. Fractal dimensions first increased and then decreased with ion fluence. The lateral correlation length decreased, while the roughness exponent increased with fluence after the threshold value. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-07T07:23:06Z DOI: 10.1063/5.0135127
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Authors:Nawaj Sarif, Sahabuddin Sarwardi Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. In the current study, the dynamics of predator–prey systems under the influence of fear effect on the reproduction of prey population and harvesting on both species has been proposed. Assessing the dynamics of the system with the combined influence of fear and harvesting for various values of n is our central objective. We present comprehensive mathematical findings that cover fundamental dynamical features, the presence of positive equilibria, and the stability of all equilibria. Hopf-bifurcating periodic solutions have been demonstrated to emerge around the positive equilibrium point, and the direction of the Hopf-bifurcating limit cycle is determined using the first Lyapunov coefficient. Furthermore, in two-parameter space, we have seen that the system experiences the Bogdanov–Takens bifurcation. Moreover, we have included predator gestation delay and noticed some chaotic dynamics in the system. In addition, we run through numerical simulations to numerically validate our mathematical findings. The article is concluded with a conclusion at the end. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-07T07:23:06Z DOI: 10.1063/5.0135181
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Authors:Massimiliano Zanin Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. We introduce a generalization of the celebrated ordinal pattern approach for the analysis of time series, in which these are evaluated in terms of their distance to ordinal patterns defined in a continuous way. This allows us to naturally incorporate information about the local amplitude of the data and to optimize the ordinal pattern(s) to the problem under study. This last element represents a novel bridge between standard ordinal analysis and deep learning, allowing the achievement of results comparable to the latter in real-world classification problems while also retaining the conceptual simplicity, computational efficiency, and easy interpretability of the former. We test this through the use of synthetic time series, generated by standard chaotic maps and dynamical models, data sets representing brain activity in health and schizophrenia, and the dynamics of delays in the European air transport system. We further show how the continuous ordinal patterns can be used to assess other aspects of the dynamics, like time irreversibility. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-07T07:23:05Z DOI: 10.1063/5.0136492
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Authors:V. B. Dorokhov, A. Runnova, O. N. Tkachenko, A. O. Taranov, G. N. Arseniev, A. Kiselev, A. Selskii, A. Orlova, M. Zhuravlev Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. In our work, we compare EEG time–frequency features for two types of K-complexes detected in volunteers performing the monotonous psychomotor test with their eyes closed. Type I K-complexes preceded spontaneous awakenings, while after type II K-complexes, subjects continued to sleep at least for 10 s after. The total number of K-complexes in the group of 18 volunteers was 646, of which of which type I K-complexes was 150 and type II K-complexes was 496. Time–frequency analysis was performed using continuous wavelet transform. EEG wavelet spectral power was averaged upon several brain zones for each of the classical frequency ranges (slow wave, [math], [math], [math], [math], [math], [math] bands). The low-frequency oscillatory activity ([math]-band) preceding type I K-complexes was asymmetrical and most prominent in the left hemisphere. Statistically significant differences were obtained by averaging over the left and right hemispheres, as well as projections of the motor area of the brain, p Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-07T07:23:04Z DOI: 10.1063/5.0143284
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Authors:Yeyin Xu, Runchao Zhao, Yinghou Jiao, Zhaobo Chen Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. A brush seal has the advantages of adapting to different vibration conditions and increasing the stability of the nonlinear rotor system. In this research, the stability and bifurcations of complex vibrations in a brush-seal rotor system are studied. An analytical seal force model is obtained through the beam theory and mutual coupling dynamics of the bristles and the rotor. The interaction between the bristles and the rotor is clearly depicted by a geometric map. Periodic and chaotic vibrations as well as the corresponding amplitude–frequency characteristics are first predicted by a numerical bifurcation diagram and 3D waterfalls. Discrete dynamic eigenvalue analysis is adopted for a detailed investigation of the stability and bifurcations of nonlinear vibrations. Jumping, quasi-periodic, and half-frequency vibrations are warned during the speeding up and down process. Four separate nonlinear vibration evolving routes are discovered. Two period-doubling bifurcation trees evolving to chaos are illustrated for the observation of global and independent periodic vibrations. Nonlinear vibration illustrations are presented through displacement orbits as well as harmonic amplitudes and phases. Chaotic vibration and unstable semi-analytical vibration solutions are compared. The obtained results and analysis methods provide new perspectives on nonlinear vibrations in the brush-seal rotor system. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-07T07:23:04Z DOI: 10.1063/5.0134907
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Authors:Stefano Pierini Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. A deterministic excitation (DE) paradigm is formulated, according to which the abrupt late Pleistocene glacial terminations correspond to the excitation, by the orbital forcing, of nonlinear relaxation oscillations (ROs) internal to the climate system in the absence of any stochastic parameterization. Specific rules are derived from the DE paradigm: they parameterize internal climate feedbacks, which, when activated by the crossing of certain tipping points, excite a RO. Such rules are then applied to the output of an energy-balance model simulating the fluctuations induced by realistic orbital forcing on the glacial state. The timing of the glacial terminations, thus, obtained in a reference simulation is found to be in good agreement with proxy records. A sensitivity analysis insures the robustness of the timing. The potential irrelevance of noise allowing DE to hold is discussed, and a possible explanation of the 100-kyr cycle problem based on DE is outlined. In conclusion, the DE paradigm provides the simplest possible dynamical systems characterization of the link between orbital forcing and glacial terminations implied by the Milankovitch hypothesis. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-07T03:45:18Z DOI: 10.1063/5.0127715
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Authors:Josselyn Gonzalez, Rosangela Follmann, Epaminondas Rosa, Wolfgang Stein Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. In this work, we study the interplay between chaos and noise in neuronal state transitions involving period doubling cascades. Our approach involves the implementation of a neuronal mathematical model under the action of neuromodulatory input, with and without noise, as well as equivalent experimental work on a biological neuron in the stomatogastric ganglion of the crab Cancer borealis. Our simulations show typical transitions between tonic and bursting regimes that are mediated by chaos and period doubling cascades. While this transition is less evident when intrinsic noise is present in the model, the noisy computational output displays features akin to our experimental results. The differences and similarities observed in the computational and experimental approaches are discussed. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-06T05:10:42Z DOI: 10.1063/5.0130874
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Authors:Shaohui Yan, Ertong Wang, Qiyu Wang Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. In order to obtain a system of higher complexity, a new fractional-order chaotic system is constructed based on the Sprott system. It is noteworthy that the system has no equilibrium point yet exhibits chaotic properties and has rich dynamical behavior. Its basic properties are analyzed by Lyapunov exponents, phase diagrams, and smaller alignment index tests. The change of its state is observed by changing parameters and order, during which the new system is found to have intermittent chaos phenomena. Surprisingly, the new proposed system has a special offset-boosting phenomenon, where only a boosting-controller makes the system undergo a multi-directional offset, and the shape of the generated hidden attractor changes. In addition, changing the initial value brings kinds of coexisting attractors in the system, which proves the existence of multistability. Because the new system is very sensitive to the initial value, the complexity of the new system is calculated based on the complexity algorithm, and the initial value with higher complexity is gained by contrast. Finally, the field programmable gate array is used to implement the actual circuit of the new system to verify its feasibility. This system provides an example for the study of fractional-order chaotic systems and a complex system for fractional-order chaotic applications. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-06T05:09:54Z DOI: 10.1063/5.0130083
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Authors:Evdokiia Slepukhina, Irina Bashkirtseva, Philipp Kügler, Lev Ryashko Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. The stochastic Hindmarsh–Rose model is studied in the parameter region where two bursting limit cycles of different types coexist. We show that under the influence of noise, transitions between basins of attractions appear, which generates stochastic bursting oscillations of mixed modes. The formation of this new regime is accompanied by anti-coherence and coherence resonances as well as by the transition to chaos. We investigate the probabilistic mechanism of the noise-driven bursting birhythmicity using the stochastic sensitivity functions and confidence domains method. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-03T02:46:48Z DOI: 10.1063/5.0134561
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Authors:E. Rybalova, S. Muni, G. Strelkova Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. We study numerically the spatiotemporal dynamics in a ring network of nonlocally coupled nonlinear oscillators, each represented by a two-dimensional discrete-time model of the classical van der Pol oscillator. It is shown that the discretized oscillator exhibits richer behavior, combining the peculiarities of both the original system and its own dynamics. Moreover, a large variety of spatiotemporal structures is observed in the network of discrete van der Pol oscillators when the discretization parameter and the coupling strength are varied. Regimes, such as the coexistence of a multichimera state/a traveling wave and a solitary state are revealed for the first time and are studied in detail. It is established that the majority of the observed chimera/solitary states, including the newly found ones, are transient toward a purely traveling wave mode. The peculiarities of the transition process and the lifetime (transient duration) of the chimera structures and the solitary state are analyzed depending on the system parameters, the observation time, initial conditions, and the influence of external noise. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-03T02:46:44Z DOI: 10.1063/5.0138207
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Authors:W. Just Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. Inspired by time-delayed feedback control, it is shown that synchronization of non-identical systems can be achieved by mutual time-delayed feedback with an asymptotically vanishing interaction. An analytic perturbation scheme is developed, which uncovers the merits as well as the constraints of such an approach. As an application, the use of the concept for a secure communication channel is considered. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-03T02:46:43Z DOI: 10.1063/5.0142803
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Authors:Qunxi Zhu, Xin Li, Wei Lin Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. Detecting unstable periodic orbits (UPOs) based solely on time series is an essential data-driven problem, attracting a great deal of attention and arousing numerous efforts, in nonlinear sciences. Previous efforts and their developed algorithms, though falling into a category of model-free methodology, dealt with the time series mostly with a regular sampling rate. Here, we develop a data-driven and model-free framework for detecting UPOs in chaotic systems using the irregularly sampled time series. This framework articulates the neural differential equations (NDEs), a recently developed and powerful machine learning technique, with the adaptive delayed feedback (ADF) technique. Since the NDEs own the exceptional capability of accurate reconstruction of chaotic systems based on the observational time series with irregular sampling rates, UPOs detection in this scenario could be enhanced by an integration of the NDEs and the ADF technique. We demonstrate the effectiveness of the articulated framework on representative examples. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-03T02:46:42Z DOI: 10.1063/5.0143839
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Authors:Gangyong Gwon, Young Sul Cho Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. Transient dynamics leading to the synchrony of a type of pulse-coupled oscillators, so-called scrambler oscillators, has previously been studied as an aggregation process of synchronous clusters, and a rate equation for the cluster size distribution has been proposed. However, the evolution of the cluster size distribution for general cluster sizes has not been fully understood yet. In this paper, we study the evolution of the cluster size distribution from the perspective of a percolation model by regarding the number of aggregations as the number of attached bonds. Specifically, we derive the scaling form of the cluster size distribution with specific values of the critical exponents using the property that the characteristic cluster size diverges as the percolation threshold is approached from below. Through simulation, it is confirmed that the scaling form well explains the evolution of the cluster size distribution. Based on the distribution behavior, we find that a giant cluster of all oscillators is formed discontinuously at the threshold and also that further aggregation does not occur like in a one-dimensional bond percolation model. Finally, we discuss the origin of the discontinuous formation of the giant cluster from the perspective of global suppression in explosive percolation models. For this, we approximate the aggregation process as a cluster–cluster aggregation with a given collision kernel. We believe that the theoretical approach presented in this paper can be used to understand the transient dynamics of a broad range of synchronizations. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-01T03:51:06Z DOI: 10.1063/5.0138880
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Authors:Eugene Tan, Shannon Algar, Débora Corrêa, Michael Small, Thomas Stemler, David Walker Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. Delay embedding methods are a staple tool in the field of time series analysis and prediction. However, the selection of embedding parameters can have a big impact on the resulting analysis. This has led to the creation of a large number of methods to optimize the selection of parameters such as embedding lag. This paper aims to provide a comprehensive overview of the fundamentals of embedding theory for readers who are new to the subject. We outline a collection of existing methods for selecting embedding lag in both uniform and non-uniform delay embedding cases. Highlighting the poor dynamical explainability of existing methods of selecting non-uniform lags, we provide an alternative method of selecting embedding lags that includes a mixture of both dynamical and topological arguments. The proposed method, Significant Times on Persistent Strands (SToPS), uses persistent homology to construct a characteristic time spectrum that quantifies the relative dynamical significance of each time lag. We test our method on periodic, chaotic, and fast-slow time series and find that our method performs similar to existing automated non-uniform embedding methods. Additionally, [math]-step predictors trained on embeddings constructed with SToPS were found to outperform other embedding methods when predicting fast-slow time series. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-01T03:50:46Z DOI: 10.1063/5.0137223
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Authors:Fatemeh Parastesh, Sridevi Sriram, Hayder Natiq, Karthikeyan Rajagopal, Sajad Jafari Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. Achieving a network structure with optimal synchronization is essential in many applications. This paper proposes an optimization algorithm for constructing a network with optimal synchronization. The introduced algorithm is based on the eigenvalues of the connectivity matrix. The performance of the proposed algorithm is compared with random link addition and a method based on the eigenvector centrality. It is shown that the proposed algorithm has a better synchronization ability than the other methods and also the scale-free and small-world networks with the same number of nodes and links. The proposed algorithm can also be applied for link reduction while less disturbing its synchronization. The effectiveness of the algorithm is compared with four other link reduction methods. The results represent that the proposed algorithm is the most appropriate method for preserving synchronization. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-01T03:50:25Z DOI: 10.1063/5.0134763
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Authors:Pedro Pessoa Abstract: Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 33, Issue 3, March 2023. It is a long held conjecture in the connection between information geometry (IG) and thermodynamics that the curvature endowed by IG diverges at phase transitions. Recent work on the IG of Bose–Einstein (BE) gases challenged this conjecture by saying that in the limit of fugacity approaching unit—where BE condensation is expected—the curvature does not diverge; rather, it converges to zero. However, as the discontinuous behavior that identifies condensation is only observed at the thermodynamic limit, a study of the IG curvature at a finite number of particles, [math], is in order from which the thermodynamic behavior can be observed by taking the thermodynamic limit ([math]) posteriorly. This article presents such a study. We find that for a trapped gas, as [math] increases, the values of curvature decrease proportionally to a power of [math], while the temperature at which the maximum value of curvature occurs approaches the usually defined critical temperature. This means that, in the thermodynamic limit, the curvature has a limited value where a phase transition is observed, contradicting the forementioned conjecture. Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science PubDate: 2023-03-01T03:50:24Z DOI: 10.1063/5.0136244
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