A class of initials-dependent dynamical systems

Ma, Jun; Wu, Fuqiang; Ren, Guo-Dong; Tang, Jun

doi:10.1016/j.amc.2016.11.004

Cited by 72 publications

(28 citation statements)

References 61 publications

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“…The 3D Lü chaotic attractor connects the 3D Lorenz attractor and 3D Chen attractor and represents the transition from one to the other. Moreover, research on chaotic systems has attracted more and more attention in the last few decades because of its great applications in many fields like secure communication [6], data encryption [7], power system protection [8], DC motor control [8][9][10], flow dynamics [11], and so on [12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

A New 3D Autonomous Continuous System with Two Isolated Chaotic Attractors and Its Topological Horseshoes

Zhou

2017

Complexity

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Based on the 3D autonomous continuous Lü chaotic system, a new 3D autonomous continuous chaotic system is proposed in this paper, and there are coexisting chaotic attractors in the 3D autonomous continuous chaotic system. Moreover, there are no overlaps between the coexisting chaotic attractors; that is, there are two isolated chaotic attractors (in this paper, named "positive attractor" and "negative attractor," resp.). The "positive attractor" and "negative attractor" depend on the distance between the initial points (initial conditions) and the unstable equilibrium points. Furthermore, by means of topological horseshoes theory and numerical computation, the topological horseshoes in this 3D autonomous continuous system is found, and the topological entropy is obtained. These results indicate that the chaotic attractor emerges in the new 3D autonomous continuous system.

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Section: Introductionmentioning

confidence: 99%

A New 3D Autonomous Continuous System with Two Isolated Chaotic Attractors and Its Topological Horseshoes

Zhou

2017

Complexity

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“…Since the physical memristor has been fabricated by Hewlett-Packard Lab in 2008 [Strukov et al, 2008], it has attracted much attention of researchers. Due to its nonvolatility, nanosize, and low power consumption, memristor can be applied in various fields, such as nonvolatile memory [Strukov, 2016], neural networks [Soudry et al, 2015;Duan et al, 2015], nonlinear chaotic circuits [Zhou et al, 2016;Wu & Wang, 2016;Yuan et al, 2016;Wang et al, 2017;Corinto & Forti, 2017;Ma et al, 2017], and so on.…”

Section: Introductionmentioning

confidence: 99%

Various Attractors, Coexisting Attractors and Antimonotonicity in a Simple Fourth-Order Memristive Twin-T Oscillator

Ling

Wang

Xin

et al. 2018

Int. J. Bifurcation Chaos

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By replacing the resistor in a Twin-T network with a generalized flux-controlled memristor, this paper proposes a simple fourth-order memristive Twin-T oscillator. Rich dynamical behaviors can be observed in the dynamical system. The most striking feature is that this system has various periodic orbits and various chaotic attractors generated by adjusting parameter b. At the same time, coexisting attractors and antimonotonicity are also detected (especially, two full Feigenbaum remerging trees in series are observed in such autonomous chaotic systems). Their dynamical features are analyzed by phase portraits, Lyapunov exponents, bifurcation diagrams and basin of attraction. Moreover, hardware experiments on a breadboard are carried out. Experimental measurements are in accordance with the simulation results. Finally, a multichannel random bit generator is designed for encryption applications. Numerical results illustrate the usefulness of the random bit generator.

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“…Spontaneously, for the initial conditions in the different color areas of the attraction basin, the phase portraits of typical coexisting attractors are obtained, as shown in Figure 4, where for the sake of observations two point attractors in Figure 4(a) are marked by two five-pointed stars. Of course, these generated coexisting attractors intersect the neighborhood of the line equilibrium point, implying that the initials-dependent dynamical system (4) [37] always oscillates in self-excited states, rather than hidden states [38][39][40].…”

Section: Coexisting Infinitely Many Attractors With Reference To Thementioning

confidence: 99%

Memristor‐Based Canonical Chua’s Circuit: Extreme Multistability in Voltage‐Current Domain and Its Controllability in Flux‐Charge Domain

et al. 2018

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This paper investigates extreme multistability and its controllability for an ideal voltage-controlled memristor emulator-based canonical Chua's circuit. With the voltage-current model, the initial condition-dependent extreme multistability is explored through analyzing the stability distribution of line equilibrium point and then the coexisting infinitely many attractors are numerically uncovered in such a memristive circuit by the attraction basin and phase portraits. Furthermore, based on the accurate constitutive relation of the memristor emulator, a set of incremental flux-charge describing equations for the memristor-based canonical Chua's circuit are formulated and a dimensionality reduction model is thus established. As a result, the initial condition-dependent dynamics in the voltage-current domain is converted into the system parameter-associated dynamics in the flux-charge domain, which is confirmed by numerical simulations and circuit simulations. Therefore, a controllable strategy for extreme multistability can be expediently implemented, which is greatly significant for seeking chaos-based engineering applications of multistable memristive circuits.

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A class of initials-dependent dynamical systems

Cited by 72 publications

References 61 publications

A New 3D Autonomous Continuous System with Two Isolated Chaotic Attractors and Its Topological Horseshoes

A New 3D Autonomous Continuous System with Two Isolated Chaotic Attractors and Its Topological Horseshoes

Various Attractors, Coexisting Attractors and Antimonotonicity in a Simple Fourth-Order Memristive Twin-T Oscillator

Memristor‐Based Canonical Chua’s Circuit: Extreme Multistability in Voltage‐Current Domain and Its Controllability in Flux‐Charge Domain

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