Research on a new 3D autonomous chaotic system with coexisting attractors

The coexisting attractors which means multiple attractors with independent domains of attraction yield simultaneously in a system is of recent interest. In this paper, we propose a new 3D autonomous quadratic chaotic system as a typical example with the presence of the coexisting attractors. Some basic dynamical properties of the system are presented. The existence of the Hopf bifurcation is established by analyzing the corresponding characteristic equation. It shows that the system coexists double Hopf bifurcation at equilibria as the parameter passes a critical value. The coexisting point, periodic, chaotic attractors in the system are numerically investigated by bifurcation diagrams, Lyapunov exponents and phase diagrams. (C) 2015 Elsevier GmbH. All rights reserved.