Multiple attractors and robust synchronization of a chaotic system with no equilibrium

Abstract This paper introduces a three-dimensional system with no equilibrium point in which the Shilnikov method is not applicable to demonstrate the chaos. The remarkable particularity of the system is that it can generate multiple attractors with different system parameters and initial values. To further understand the complex dynamics, some basic properties of the system are studied theoretically and numerically. Simultaneously, by considering the sensibility to system parameter and initial value, a robust synchronization scheme of this chaotic system is proposed. Sufficient conditions to guarantee synchronization are given in the sense of H ∞ stability theory, numerical simulations are performed to further verify the effectiveness.