Symmetric coexisting attractors and extreme multistability in chaotic system

Abstract

In this paper, a new four-dimensional (4D) chaotic system with two cubic nonlinear terms is proposed. The most striking feature is that the new system can exhibit completely symmetric coexisting bifurcation behaviors and four symmetric coexisting attractors with the same Lyapunov exponents in all parameter ranges of the system when taking different initial states. Interestingly, these symmetric coexisting attractors can be considered as unusual symmetrical rotational coexisting attractors, which is a very fascinating phenomenon. Furthermore, by using a memristor to replace the coupling resistor of the new system, an interesting 4D memristive hyperchaotic system with one unstable origin is constructed. Of particular surprise is that it can exhibit four groups of extreme multistability phenomenon of infinitely many coexisting attractors of symmetric distribution about the origin. By using phase portraits, Lyapunov exponent spectra, and coexisting bifurcation diagrams, the dynamics of the two systems are fully analyzed and investigated. Finally, the electronic circuit model of the new system is designed for verifying the feasibility of the new chaotic system.