Extremely rich dynamics in a memristor-based chaotic system

Abstract

By introducing a memristor to the jerk system, a four-dimensional (4D) chaotic system is proposed. This system has five line equilibrium points with different stability. The extremely rich dynamic behaviors are studied by numerical simulation and theoretical analysis. Specifically, transient dynamics of coexisting chaotic attractors with different amplitudes at different time scales are found. And extreme multistability of mirror symmetric chaotic attractors, different scroll or amplitude of chaotic attractors, and different periodic attractors can be observed by selecting appropriate parameters and initial conditions. It is also found that the initial condition of the memristor can be used as the controller to realize the offset boost of the chaotic attractor. Then, the HSVII method, which includes state increment integral transformation and linear transformation, is used to reduce the dimension of the system and realize the transformation of correlation dynamics of initial condition into correlation dynamics of system parameter. It is proved numerically that the HSVII method is effective for the multistability analysis of the memristive chaotic system.