Abundant Coexisting Multiple Attractors’ Behaviors in Three-Dimensional Sine Chaotic System

Abstract

This paper presents a novel and simple three-dimensional (3-D) chaotic system by introducing two sine nonlinearities into a simple 3-D linear dynamical system. The presented sine system possesses nine equilibrium points consisting of five index-2 saddle foci and four index-1 saddle foci which allow the coexistence of various types of disconnected attractors, also known as multistability. The coexisting multiple attractors are depicted by the phase plots and attraction basins. Coexisting bifurcation modes triggered by different initial values are numerically simulated by two-dimensional bifurcation and complexity plots under two sets of initial values and one-dimensional bifurcation plots under three sets of initial values, which demonstrate that the abundant coexisting multiple attractors’ behaviors in the presented sine system are related not only to the system parameters but also to the initial values. A simulation-oriented circuit model is synthesized, and PSIM (power simulation) screen captures well validate the numerical simulations.