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.

Keywords

• Chaotic system
• coexisting attractors
• Lyapunov exponents
• equilibrium