Coexisting attractors, circuit realization and impulsive synchronization of a new four-dimensional chaotic system

Abstract

This paper presents a new four-dimensional chaotic system with three nonlinearities and two equilibria. The most striking feature of the new system is that it has different types of asymmetric coexisting attractors. Simulation experiments are used to study the complex dynamic behaviors of the system. The chaos, period-doubling bifurcation, coexisting attractors with respect to system parameters and initial values are found in the system. It shows that the system has coexisting chaotic attractors, coexisting periodic attractors, coexisting chaotic and periodic attractors. The electronic circuit is applied to implement the chaotic attractor and coexisting attractors for studying the physical significance of the system. In addition, we consider the synchronization of the system by using the impulsive control method. Some synchronization criteria are established via theoretical analysis and simulation example.