The simplest 4-D chaotic system with line of equilibria, chaotic 2-torus and 3-torus behaviour

<p>A new chaotic system with line equilibrium is introduced in this paper. This system consists of five terms with two transcendental nonlinearities and two quadratic nonlinearities. Various tools of dynamical system such as phase portraits, Lyapunov exponents, Kaplan-Yorke dimension, bifurcation diagram and Poincarè map are used. It is interesting that this system has a line of fixed points and can display chaotic attractors. Next, this paper discusses control using passive control method. One example is given to insure the theoretical analysis. Finally, for the new chaotic system, An electronic circuit for realizing the chaotic system has been implemented. The numerical simulation by using MATLAB 2010 and implementation of circuit simulations by using MultiSIM 10.0 have been performed in this study.</p>

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Crisis in Amplitude Control Hides in Multistability

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127416502333 ◽

2016 ◽

Vol 26 (14) ◽

pp. 1650233 ◽

Cited By ~ 19

Author(s):

Chunbiao Li ◽

Julien Clinton Sprott ◽

Hongyan Xing

Keyword(s):

Chaotic System ◽

Basins Of Attraction ◽

The Other ◽

Symmetric System ◽

Partial Amplitude ◽

Total Amplitude ◽

Amplitude Control ◽

Amplitude Parameter ◽

New Chaotic System ◽

Line Of Equilibria

A crisis of amplitude control can occur when a system is multistable. This paper proposes a new chaotic system with a line of equilibria to demonstrate the threat to amplitude control from multistability. The new symmetric system has two coefficients for amplitude control, one of which is a partial amplitude controller, while the other is a total amplitude controller that simultaneously controls the frequency. The amplitude parameter rescales the basins of attraction and triggers a state switch among different states resulting in a failure of amplitude control to the desired state.

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Generating Four-Wing Hyperchaotic Attractor and Two-Wing, Three-Wing, and Four-Wing Chaotic Attractors in 4D Memristive System

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127417500274 ◽

2017 ◽

Vol 27 (02) ◽

pp. 1750027 ◽

Cited By ~ 40

Author(s):

Ling Zhou ◽

Chunhua Wang ◽

Lili Zhou

Keyword(s):

Chaotic System ◽

Three Dimensional ◽

Phase Portraits ◽

Chaotic Attractors ◽

Hyperchaotic System ◽

Multiple Attractors ◽

System A ◽

Dynamical Behaviors ◽

Memristive System ◽

Line Of Equilibria

By adding only one smooth flux-controlled memristor into a three-dimensional (3D) pseudo four-wing chaotic system, a new real four-wing hyperchaotic system is constructed in this paper. It is interesting to see that this new memristive chaotic system can generate a four-wing hyperchaotic attractor with a line of equilibria. Moreover, it can generate two-, three- and four-wing chaotic attractors with the variation of a single parameter which denotes the strength of the memristor. At the same time, various coexisting multiple attractors (e.g. three-wing attractors, four-wing attractors and attractors with state transition under the same system parameters) are observed in this system, which means that extreme multistability arises. The complex dynamical behaviors of the proposed system are analyzed by Lyapunov exponents (LEs), phase portraits, Poincaré maps, and time series. An electronic circuit is finally designed to implement the hyperchaotic memristive system.

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