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Similar Journals
 Nonlinear DynamicsJournal Prestige (SJR): 1.468 Citation Impact (citeScore): 4Number of Followers: 20      Hybrid journal (It can contain Open Access articles) ISSN (Print) 1573-269X - ISSN (Online) 0924-090X Published by Springer-Verlag  [2652 journals]
• Nonlinear phenomena of contact in multibody systems dynamics: a review
• Abstract: In the present work, an introduction to the contact phenomena in multibody systems is made. The different existing approaches are described, together with their most distinctive features. Then, the term of coefficient of restitution is emphasized as a tool to characterize impact events and the algorithm for calculating the relative indentation between two convex-shaped bodies is developed. Subsequently, the main penalty contact models developed in the last decades are presented and developed, analysing their advantages and drawbacks, as well as their respective applications. Furthermore, some models with specific peculiarities that could be useful to the reader are included. The aim of this work is to provide a resource to the novice researcher in the field to facilitate the choice of the appropriate contact model for their work.
PubDate: 2021-03-14

• Directed vector visibility graph from multivariate time series: a new
method to measure time series irreversibility
• Abstract: As a practical tool, visibility graph provides a different perspective to characterize time series. In this paper, we present a new visibility algorithm called directed vector visibility graph and combine it with the Kullback–Leibler divergence to measure the irreversibility of multivariable time series. T directed vector visibility algorithm converts the time series into a directed network. Subsequently, the ingoing and outgoing degree distributions of the directed network can be got to calculate the Kullback–Leibler divergence, which will be applied to assess the level of irreversibility of the time series. This is a simple and effective method without any special symbolic process. The numerical results from various types of systems are used to validate that this method can accurately distinguish reversible time series from those irreversible ones. Finally, we employ this method to estimate the irreversibility of financial time series and the results show that our method is efficient to analyze the financial time series irreversibility.
PubDate: 2021-03-13

• Coexisting firing patterns and phase synchronization in locally active
memristor coupled neurons with HR and FN models
• Abstract: Local activity is regarded as the origin of complexity. In this study, a locally active memristor with coexisting two stable pinched hysteresis loops and two local activity regions is proposed. Its nonvolatile memory, as well as locally active characteristics, is validated by the power-off plot and DC V–I plot. Based on two-dimensional Hindmarsh–Rose and two-dimensional Fitzhugh–Nagumo neurons, a simple neural network is constructed by connecting the two neurons with the locally active memristor. Coexisting multiple firing patterns under different initial conditions are investigated by considering the coupling strength as a unique controlled parameter. The results suggest that the system exhibits coexisting periodic and chaotic bursting firing patterns as well as coexisting two periodic firing patterns with different topologies. Furthermore, state switching without parameters is also explored. In particular, phase synchronization of the memristor synapse-coupled neurons is discussed, which implies that two nonidentical neurons gradually become phase synchronized with the increase in the coupling strength. In order to confirm the effectiveness of numerical simulations, circuit simulations are included.
PubDate: 2021-03-13

• COVID-19 dynamics considering the influence of hospital infrastructure: an
investigation into Brazilian scenarios
• Abstract: COVID-19 dynamics is one of the most relevant subjects nowadays, and, in this regard, mathematical modeling and numerical simulations are of special interest. This paper describes COVID-19 dynamics based on a novel version of the susceptible–exposed–infectious–removed model. Removed population is split into recovered and death populations allowing a better comprehension of real situations. Besides, the total population is reduced based on the number of deaths. Hospital infrastructure is also included into the mathematical description allowing the consideration of collapse scenarios. Initially, a model verification is carried out calibrating system parameters with data from China outbreak that is considered a benchmark due the availability of data for the entire cycle. Afterward, Brazil outbreak is of concern, calibrating the model and developing numerical simulations. Results show several scenarios highlighting the importance of social isolation and hospital infrastructure. System dynamics has a strong sensitivity to transmission rate showing the importance of numerical simulations to guide public health decision strategies. Results also show that complex dynamical responses can emerge due to the oscillations of the transmission rate, being associated with distinct infection subsequent waves.
PubDate: 2021-03-13

• A projection-based algorithm for optimal formation and optimal matching of
multi-robot system
• Abstract: In this paper, the optimal formation and optimal matching of a multi-robot system are investigated with a projection-based algorithm designed to get the optimal formation moving in real time. The formation-related optimization problem is proposed under the consideration of two cases: the free formation and the formation with anchor(s). For the latter, equality constraints are formulated for the anchor, and the objective of the optimal formation is to minimize the total distance to the initial formation of the multi-robot system. Here, the objective function with mixed norm is considered to get a compact formation. Sufficient conditions on the design parameter for global convergence of the proposed algorithm are provided in the theoretical results. Furthermore, the projection particle swarm optimizer is investigated for getting the optimal matching between the initial/intermediate formation and the optimal formation. Finally, simulations on several numerical examples are presented to validate the effectiveness of the proposed method.
PubDate: 2021-03-13

• On the soliton solutions for an intrinsic fractional discrete nonlinear
electrical transmission line
• Abstract: This paper focuses on finding soliton solutions for an intrinsic fractional discrete nonlinear electrical transmission lattice. Our investigation is based on the fact that for a realistic system, the electrical characteristics of a capacitor (and an inductor via skin effect) should include a fractional-order time derivative. In this respect for the model under consideration, we derive a fractional nonlinear partial differential equation for the voltage dynamics by applying the Kirchhoff’s laws. It is realized that the behavior of new soliton solutions obtained is influenced by the fractional-order time derivative as well as the coupling values. The fractional order also modifies the propagation velocity of the voltage wave notwithstanding their structure and tends to set up localized structure for low coupling parameter values. However, for a high value of the coupling parameter, the fractional order is less seen on the shapes of the new solitary solutions that are analytically derived. Several methods such as the Kudryashov method, the $$(G'/G)$$ -expansion method, the Jacobi elliptical functions method and the Weierstrass elliptic function expansion method led us to derive these solitary solutions while using the modified Riemann–Liouville derivatives in addition to the fractional complex transform. An insight into the overall dynamics of our network is provided through the analysis of the phase portraits.
PubDate: 2021-03-11

• Motion and shape control of soft robots and materials
• Abstract: A continuum-based approach for simultaneously controlling the motion and shape of soft robots and materials (SRM) is proposed. This approach allows for systematically computing the actuation forces for arbitrary desired SRM motion and geometry. In order to control both motion and shape, the position and position gradients of the absolute nodal coordinate formulation (ANCF) are used to formulate rheonomic specified trajectory and shape constraint equations, used in an inverse dynamics procedure to define the actuation control forces. Unlike control of rigid-body systems which requires a number of independent actuation forces equal to the number of the joint coordinates, the SRM motion/shape control leads to generalized control forces which need to be interpreted differently in order to properly define the actuation forces. While the definition of these motion/shape control forces is demonstrated using air pressure actuation commonly used in the SRM control, the proposed procedure can be applied to other SRM actuation types. The approaches for determining the actuation pressure in the two cases of space-dependent and constant pressures are outlined. Effect of the change in the surface geometry on the actuation pressure is accounted for using Nanson’s formula. The obtained numerical results demonstrate that the motion and shape can be simultaneously controlled using the new actuation force definitions.
PubDate: 2021-03-10

• On the escape of a resonantly excited couple of particles from a potential
well
• Abstract: The escape dynamics of a damped system of two coupled particles in a truncated potential well under biharmonic excitation are investigated. It is assumed that excitation frequencies are tuned to the modal natural frequency of the relative motion and to the modal frequency of the centre of mass on the bottom of the potential well. Although the escape is essentially a non-stationary process, the critical force strongly depends on the stationary amplitude of the relative vibrations within the pair of masses. The characteristic escape curve for the critical force moves up on the frequency-escape threshold plane with increasing relative vibrations, which can be interpreted as a stabilizing effect due to the high-frequency excitation. To obtain the results, new modelling techniques are suggested, including the reduction in the effect of the high-frequency excitation using a probability density function-based convolution approach and an energy-based approach for the description of the evolution of the slow variables. To validate the method, the coupled pair of particles is investigated with various model potentials.
PubDate: 2021-03-10

• Methodology proposal of ADHD classification of children based on cross
recurrence plots
• Abstract: Dealing with electroencephalogram signals (EEG) is often not easy. The lack of predicability and complexity of such non-stationary, noisy and high-dimensional signals is challenging. Cross recurrence plots (CRP) have been used extensively to deal with the detection of subtle changes in signals, even when the noise is embedded in the signal. In this contribution, a total of 121 children performed visual attention experiments and a proposed methodology using CRP and a Welch Power Spectral Distribution have been used to classify then between those who have ADHD and the control group. Additional tools were presented to determine to which extent this methodology is able to classify accurately and avoid misclassifications, thus demonstrating that this methodology is feasible to classify EEG signals from subjects with ADHD. The experimental results indicate that the proposed methodology shows higher accuracy in comparison with methods proposed by other authors, providing that the correct recurrence tools are selected. Also, this methodology does not require extensive training such as the methods proposed using classical machine learning algorithms. Furthermore, this proposed methodology shows that it is not required to manually discriminate events among the EEG electrodes since CRP can detect even the smallest changes in the signal even when it has embedded noise. Lastly, the results were compared with baseline machine learning methods to prove experimentally that this methodology is consistent and the results repeatable. Given the right CRP metrics, an accuracy of up to 97.25% was achieved, indicating that this methodology outperformed many of the state-of-the-art techniques.
PubDate: 2021-03-10

• Chemical and biological control of parasite-borne disease Schistosomiasis:
An impulsive optimal control approach
• Abstract: This article deals in a continuous Schistosomiasis transmission model involving hosts human and freshwater snail, and two free living Schistosoma larva forms Miracidia and Cercariae. Along with derivation of basic reproduction number and standard equilibrium analysis, Hopf bifurcation phenomenon is demonstrated analytically and numerically. Parameter sensitivity analysis of system solution has been used to identify significant parameters for the change of disease dynamics. Impulsive optimal control of the same system, adding combined biological and chemical control of snail population to minimize human infection is undertaken. Snail natural predator crayfish is used for biological control and molluscicide is used for chemical control, where both controls are released in water periodically for finite number of times. Mathematically, the continuous system is converted to a discrete-continuous hybrid control problem applying Pontryagin’s Maximum Principle. The optimum solution revealed the quantity of each control to be released at each time point. The control analysis identified parameters crucial to success of combined control.
PubDate: 2021-03-10

• Grid cell activity and path integration on 2-D manifolds in 3-D space
• Abstract: Spatial navigation relies on various types of neurons to form an internal representation in the brain of the external world. Among them, grid cells are generally believed to serve as an invariant metric system by their spatially periodic firing fields. But how this metrical coordinate system is organized in three-dimensional (3-D) real world remains a mystery, since most researches merely concerned the encoding scheme on the horizontal plane. We computationally explored the activity pattern of grid cell in the medial entorhinal cortex of crawling animal in 3-D space. By including the presumably referring signals of gravity and animal’s body plane, grid cell firing fields on curved surfaces were produced based on the novel gravity-modulated oscillatory model. The results can account for the known experimental recordings and predict a mosaic-type grid code consisting of dynamically rotated planar arrangements. We further analyzed the path integration mechanism and derived the condition to ensure the invariant grid fields on any curved surface in 3-D space. It turns out that if the grid code is indeed not fully volumetric, it may become trajectory-dependent in 3-D space. And thus for crawling animals, 3-D grid fields could be degenerated and impaired, causing the path integration and distance measurement inaccurate. Besides, the volumetric firing fields were also discussed, although it is more suitable for flying or aquatic animals. This work can help us understand the intrinsically different spatial codes and navigating abilities among species with various locomotion modes and provide new insights of how the actual physical world is represented in the brain.
PubDate: 2021-03-09

• Dynamics of COVID-19 transmission with comorbidity: a data driven
modelling based approach
• Abstract: An outbreak of the COVID-19 pandemic is a major public health disease as well as a challenging task to people with comorbidity worldwide. According to a report, comorbidity enhances the risk factors with complications of COVID-19. Here, we propose and explore a mathematical framework to study the transmission dynamics of COVID-19 with comorbidity. Within this framework, the model is calibrated by using new daily confirmed COVID-19 cases in India. The qualitative properties of the model and the stability of feasible equilibrium are studied. The model experiences the scenario of backward bifurcation by parameter regime accounting for progress in susceptibility to acquire infection by comorbidity individuals. The endemic equilibrium is asymptotically stable if recruitment of comorbidity becomes higher without acquiring the infection. Moreover, a larger backward bifurcation regime indicates the possibility of more infection in susceptible individuals. A dynamics in the mean fluctuation of the force of infection is investigated with different parameter regimes. A significant correlation is established between the force of infection and corresponding Shannon entropy under the same parameters, which provides evidence that infection reaches a significant proportion of the susceptible.
PubDate: 2021-03-08

• Nonlinear normal modes and optimization of a square root nonlinear energy
sink
• Abstract: Since the vibration mitigation of nonlinear energy sinks (NESs) needs multi-objective optimization, this paper aims to address this issue with efficient multi-objective particle swarm optimization (MOPSO) methods. A non-polynomial NES model, namely a square root NES (SRNES), is targeted for multi-objective optimization and dynamical analysis on an impulsively excited linear oscillator (LO) and compared with the corresponding polynomial model. Different MOPSO methods are developed to balance the mass and dissipation efficiency of SRNESs by utilizing weighted ranking, external archive, and non-dominated sorting. And nonlinear normal modes (NNMs) are extended for the analysis of SRNESs. The optimization results show the efficient targeted energy transfer (TET) and high robustness of the bistable SRNES in different LO initial and damping conditions. Specifically, more than 95% energy absorption can be easily witnessed, even in a small mass ratio (around 0.003), but the amplitude of the SRNES can be very large. The principal manifestation of the optimal TET is 1:1 resonance capture along with considerable low-frequency components of the SRNES. The optimization results of the SRNESs and the linear vibration absorbers show high similarities, while with a large mass ratio, the SRNESs possess broader range of spring stiffness. In the comparison of the two NES models, the differences are found in potential energy surfaces, NNMs, in-well motion, and vibration attenuation performance. Besides, the SRNESs can be divided into two groups in terms of the conservative dynamics, which can be explained by the polynomial model. The frequency component of in-phase NNMs dominates in the conservative and dissipative dynamics of the SRNESs, which lead to the transition of NNMs in the dissipative dynamics. In summary, the efficient MOPSO methods can be designed for different needs of vibration suppression and structure cost. Furthermore, it is important to directly analyze the non-polynomial nonlinear vibration, because transforming non-polynomial models into polynomial ones may lead to unreasonable or imprecise results. Finally, the NES damping structure and the NES performance in small mass conditions should be enhanced.
PubDate: 2021-03-08

• Study on dynamical behavior of multiple lump solutions and interaction
between solitons and lump wave
• Abstract: In this paper, a new (3+1)-dimensional Hirota bilinear equation in fluids is investigated. The interaction solutions of lump and N-soliton ( $$N>1$$ ) are obtained. When $$N=2, 3, 4$$ , new dynamical behavior is analyzed. The interaction of lump and periodic solutions is studied, including lump and 1-periodic solution and lump and 2-periodic solution. The interaction of lump, periodic and 1-soliton solutions is discussed. Finally, we obtain the multi-lump solutions, including 1-order, 2-order and 3-order lump solutions.
PubDate: 2021-03-08

• Adaptive fuzzy finite-time control of stochastic nonlinear systems with
actuator faults
• Abstract: This paper considers the finite-time control problem for a class of nonlinear stochastic systems with actuator faults/failure. A fast convergence feedback control algorithm based on backstepping finite-time command filtering is proposed. Under the framework of adaptive feedback, the fuzzy logic system is used to deal with the uncertainties of the system. Taking into account the actuator faults of both loss of effectiveness and lock-in-place, an adaptive fuzzy controller is developed. Since there is no need to calculate the derivative of the virtual control signal, the presented scheme overcomes the “explosion of complexity” problem inherent in conventional methods. A compensation mechanism is also introduced to compensate for errors caused by the filter. The proposed method ensures not only that all signals of the closed-loop system are finite-time bounded, but also that the tracking error converges to a small neighborhood around the origin. The effectiveness of the proposed method is demonstrated in the simulation results.
PubDate: 2021-03-08

• Non-fragile extended dissipative state estimation for delayed
discrete-time neural networks: application to quadruple tank process model

• Abstract: This paper deals with the non-fragile state estimator design to study the robust extended dissipativity criterion for a class of discrete-time neural networks (DNNs) involving uncertainties as well as time-varying delay components. The requisite of the proposed problem is to design a proper state estimator such that the dynamics of the corresponding estimation error is extended dissipative having external disturbance and unpredictable fragility performance. By constructing an appropriate Lyapunov–Krasovskii functional (LKF), the sufficient conditions for the extended dissipativity performance of the error system obtained by means of the proposed DNNs and its estimator which includes the $$H_{\infty }$$ performance, $$L_{2}-L_{\infty }$$ performance, passivity and dissipativity performance in a unified framework. The established theoretical results are expressed in terms of linear matrix inequalities (LMIs) that can be easily checked by using the standard numerical softwares. In order to analyze the applicability and effectiveness of the proposed theoretical results, numerical examples including a quadruple tank process (QTP) system model have been illustrated with simulation results.
PubDate: 2021-03-07

• Functional brain network dynamics based on the Hindmarsh–Rose model
• Abstract: In order to reveal the dynamics of brain network, we proposed a new research method based on the Hindmarsh–Rose model. In the method, a neural network model was developed by constructing a functional brain network topology based on functional magnetic resonance imaging resting-state data and using Hindmarsh–Rose neurons as nodes in place of the brain regions belonging to the functional brain network. The dynamics of the functional brain network were investigated using the dynamics model. The simulation results showed that the dynamic behaviors of the brain regions in the functional brain network could be divided into three types: stable, chaotic, and periodical bursts. A state space was introduced to analyze the dynamic behavior of the brain regions in the network. We find that increasing excitation and mutual connection strength among brain regions enhanced network communication capabilities in the state space. Both the periodic and stable modes exhibited stronger communication capabilities than the chaotic mode. Despite individual differences in the dynamics of brain regions among subjects, brain regions in the periodic mode were highly consistent and corresponded to key regions of the default mode network in the resting state.
PubDate: 2021-03-07

• On the robust Newton’s method with the Mann iteration and the artistic
patterns from its dynamics
• Abstract: There are two main aims of this paper. The first one is to show some improvement of the robust Newton’s method (RNM) introduced recently by Kalantari. The RNM is a generalisation of the well-known Newton’s root finding method. Since the base method is undefined at critical points, the RNM allows working also at such points. In this paper, we improve the RNM method by applying the Mann iteration instead of the standard Picard iteration. This leads to an essential decrease in the number of root finding steps without visible destroying the sharp boundaries among the basins of attractions presented in polynomiographs. Furthermore, we investigate visually the dynamics of the RNM with the Mann iteration together with the basins of attraction for varying Mann’s iteration parameter with the help of polynomiographs for several polynomials. The second aim of this paper is to present the intriguing polynomiographs obtained from the dynamics of the RNM with the Mann iteration under various sequences used in this iteration. The obtained polynomiographs differ considerably from the ones obtained with the RNM and are interesting from the artistic perspective. Moreover, they can easily find applications in wallpaper or fabric design.
PubDate: 2021-03-07

• Robust $$H_{\infty }$$ H ∞ adaptive output feedback sliding mode control
for interval type-2 fuzzy fractional-order systems with actuator faults
• Abstract: This paper addresses the $$H_{\infty }$$ adaptive output feedback sliding mode fault-tolerant control problem for uncertain nonlinear fractional-order $$\hbox {systems}$$ (FOSs) with $$0<\alpha <1$$ . The interval type-2 Takagi–Sugeno model is employed to represent the FOSs. Adaptive laws are designed to estimate the upper bounds of the nonlinear terms and mismatched disturbances. A reduced dimension sliding surface is constructed based on system output. A sufficient condition is established in terms of linear matrix inequalities to guarantee the stability of the sliding mode. Then, a control scheme based on fractional-order reaching law is proposed to make the resulting control system reach the sliding mode surface in a finite time. The effectiveness of proposed methods is illustrated by a numerical simulation example.
PubDate: 2021-03-07

• Arch microbeam bifurcation gas sensors
• Abstract: We investigate the potential of electrostatic initially curved microbeams to serve as bifurcation gas sensors. Toward that end, we develop static and dynamic reduced-order models of those beams and investigate their nonlinear response. Unlike many models, ours takes into account naturally occurring asymmetries present in fabricated microbeams. We conduct a detailed analysis of the nonlinear dynamics of arch beams focused on their exploitation for inertial sensing applications. The static response reveals that accounting for asymmetry replaces the saddle-node bifurcation, where snap-back occurs, with a symmetry-breaking bifurcation and reduced the voltage range for bistability. The dynamic analysis shows that a symmetry-breaking bifurcation precludes dynamic snap-through in the vicinity of superharmonic resonance, thereby significantly reducing the amplitude of those oscillations. It also shows evidence of a period-doubling bifurcation route to chaos in the vicinity of primary resonance. Based on these findings, we present a novel phase-based bifurcation gas sensor. The proposed detection mechanism allows, for the first time, the use of transition from regular periodic to chaotic motions in inertial sensing of gases. The sensor operation point is set close to the cyclic-fold bifurcation in the vicinity of primary resonance. When mass added by gas immobilization on the detector layer exceeds a threshold, the sensor oscillations abruptly transition from regular periodic motions to chaotic motions. This change can be detected by monitoring the response phase angle as it undergoes a major shift from slow variation within a limited range to fast variation over the full range due to the stretching and folding of the chaotic attractor. The proposed detection mechanism allows the sensor to operate in binary (digital) and analog modes. This is achieved by evaluating the RMS of the response phase angle $$\bar{\varphi }$$ and using it to either detect a gas concentration in excess of a safe threshold as an abrupt jump in $$\bar{\varphi }$$ or via a calibration curve relating $$\bar{\varphi }$$ to the gas concentration. The minimum detectable mass of the sensor is found to be 120 pg.
PubDate: 2021-03-07

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