Hidden and self-excited coexisting attractors in a Lorenz-like system with two equilibrium points

Cang, Shijian; Li, Yue; Zhang, Ruiye; Wang, Zenghui

doi:10.1007/s11071-018-4570-x

Cited by 72 publications

(20 citation statements)

References 48 publications

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“…In recent years, the phenomenon of coexisting behaviors [26][27][28][29] has become a very important research topic and received extensive attention. Coexisting behavior is an intricate dynamical phenomenon that contains different kinds of stable dyanmical behaviors in the same nonlinear system under different initial states [30].…”

Section: Introductionmentioning

confidence: 99%

Firing multistability in a locally active memristive neuron model

et al. 2020

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The theoretical, numerical and experimental demonstrations of firing dynamics in isolated neuron are of great significance for the understanding of neural function in human brain. In this paper, a new type of locally active and non-volatile memristor with three stable pinched hysteresis loops is presented. Then a novel locally active memristive neuron model is established by using the locally active memristor as a connecting autapse, both firing patterns and multistability in this neuronal system are investigated. We have confirmed that, on the one hand, the construced neuron can generate multiple firing patterns like periodic bursting, periodic spiking, chaotic bursting, chaotic spiking, stochastic bursting, transient chaotic bursting and transient stochastic bursting. On the other hand, the phenomenon of firing multistability with coexisting four kinds of firing patterns can be observed via changing its initial states. It is worth noting that the proposed neuron exhibits such firing multistability previously unobserved in single neuron model. Finally, an electric neuron is designed and implemented, which is extremely useful for the practical scientific and engineering applications. The results captured from neuron hardware experiments match well with the theoretical and numerical simulation results.

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Section: Introductionmentioning

confidence: 99%

Firing multistability in a locally active memristive neuron model

et al. 2020

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“…As a type of classically chaotic system, Lorenz system family has been extensively studied and applied in the past decades. However, most of the work focused on the study of dynamic characteristics at the same timescale [6][7][8], and the multi-timescale dynamics of Lorenz system family is rarely reported. Therefore, "what kind of dynamic behavior can Lorenz system family with multi timescale and multi-frequency periodic excitation exhibit?"…”

Section: Introductionmentioning

confidence: 99%

Multi-bifurcation cascaded bursting oscillations and mechanism in a novel 3D non-autonomous circuit system with parametric and external excitation

Wang

Zhang

et al. 2021

Nonlinear Dyn

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In this paper, multi-timescale dynamics and the formation mechanism of a 3D non-autonomous system with two slowly varying periodic excitations are systematically investigated. Interestingly, the system shows novel multibifurcation cascaded bursting oscillations (MBCBOs) when the frequency of the two excitations is much lower than the mean frequency of the original system (MFOS). For instance, periodic, quasi-periodic and chaotic bursting oscillations induced by a variety of cascaded bifurcations are first observed, and the phenomenon of spiking transfer is also revealed. Besides, stability and local bifurcations of the system are comprehensively investigated to analyze the mechanism of the observed MBCBOs, in which bifurcation diagram, Lyapunov exponents, time series, phase portraits, and transformed phase diagrams are used. Finally, through a circuit simulation and hardware experiment, these complex dynamics phenomena are verified physically.

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“…Among other topics, one of the new-brand categories of studying the nonlinear system's dynamic is hidden attractors [49][50][51]. Based on the studies declared in [52][53][54], generally, two principal categories can be defined for the system's attractors: self-excited and hidden attractors.…”

Section: Introductionmentioning

confidence: 99%

A New Circumscribed Self‐Excited Spherical Strange Attractor

Ramamoorthy¹,

Jamal

Hussain

et al. 2021

Complexity

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Studying new chaotic flows with specific characteristics has been an open-ended field of exploring nonlinear dynamics. Investigation of chaotic flows is an area of research that has been taken into consideration for many years; thus, it helps in a better understanding of the chaotic systems. In this paper, an original chaotic 3D system, which has not been investigated yet, is presented in spherical coordinates. A unique feature of the proposed system is that its velocity becomes zero for a specific value of the radius variable. Hence, the system’s attractor is expected to be stuck on one side of a plane in spherical coordinates and inside or outside a sphere in the corresponding Cartesian coordinates. It means that the attractor cannot pass through the sphere or even touch it. The introduced system owns two unstable equilibria and a self-excited strange attractor. The 1D and 2D system’s bifurcation diagrams concerning the alteration of two bifurcation parameters are plotted to investigate the system’s dynamical properties. Moreover, the system’s Lyapunov exponents in the corresponding period of bifurcation parameters are calculated. Then, two 2D basins of attraction for two different third dimension values are explored. Based on the basin of attraction, it can be found that the sphere has attraction itself, partially, and some initial conditions are led to the sphere, not to the strange attractor. Ultimately, the connecting curves of the proposed system are explored to find an informative 1D set in addition to the system’s equilibria.

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Hidden and self-excited coexisting attractors in a Lorenz-like system with two equilibrium points

Cited by 72 publications

References 48 publications

Firing multistability in a locally active memristive neuron model

Firing multistability in a locally active memristive neuron model

Multi-bifurcation cascaded bursting oscillations and mechanism in a novel 3D non-autonomous circuit system with parametric and external excitation

A New Circumscribed Self‐Excited Spherical Strange Attractor

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