Constructing Chaotic System With Multiple Coexisting Attractors

Abstract

This paper reports the method for constructing multiple coexisting attractors from a chaotic system. First, a new four-dimensional chaotic system with only one equilibrium and two coexisting strange attractors is established. By using bifurcation diagrams and Lyapunov exponents, the dynamical evolution of the new system is presented. Second, a feasible and effective method is applied to construct an infinite number of coexisting attractors from the new system. The core of this method is to batch replicate the attractor of the system in phase space via generating multiple invariant sets and the generation of invariant sets depends on the equilibria, which can be extended by using some simple functions with multiple zeros. Finally, we give some numerical results of the appearance of multiple coexisting attractors in the system with sine and sign functions for demonstrating the effectiveness of the method.

Using the 0-1 Test for Chaos in Nonlinear Continuous Systems With Two Varying Parameters: Parallel Computations

“…The parameter R is the resistance value in the simple arc circuits shown in Fig.2, whose mathematical model is given in Appendix B (see (2)). Thus, for any fixed value of R in the interval [5,25] we obtain the corresponding K value from the interval [0, 1]. The values of K close to 0 indicate periodic time series, while those close to 1 are obtained for chaotic ones.…”

Coexistence of Multiple Points, Limit Cycles, and Strange Attractors in a Simple Autonomous Hyperjerk Circuit with Hyperbolic Sine Function

“…A multistable system is a system with various coexisting stable states (chaotic, point, and periodic state) under the same system parameters, with different initial conditions. In recent years, the phenomenon of multistability phenomenon has been reported in many nonlinear dynamic systems [13,[36][37][38][39][40][41][42][43][44][45][46].…”

Extreme Multistability in Simple Area-Preserving Map

“…Because of the multi-stable line or plane equilibrium aroused by memristors, initial condition-relied extreme multistability with complex bifurcation routes was emerged in memristor-based chaotic circuits and systems [21]. By contrast, due to the infinitely many isolated equilibria caused by periodic nonlinearities, initial condition-boosting infinite attractors were found in some periodic function-based offset-boostable dynamical systems [22], [23]. Furthermore, by introducing a memristor with periodic memductance into an offset-boostable linear system, a new memristive chaotic system was presented [24], [25], from which extreme multistability with the initial condition-relied bifurcation route to chaos and boosting bifurcation dynamics were disclosed.…”