5D Hyper-Chaotic System with Multiple Types of Equilibrium Points

A chaotic system with various equilibrium types has rich dynamic behaviors. Its state can switch flexibly among different families of attractors, which is beneficial to the practical applications. So it has been widely concerned in recent years. In this paper, a new 5D hyper-chaotic system is proposed. The important characteristic of the system is that it may have multiple types of equilibrium points by changing system parameters, namely, linear equilibrium point, no equilibrium point, non-hyperbolic unstable equilibrium point and stable hyperbolic-type equilibrium point. Furthermore, there are hyper-chaotic phenomena and multi-stability about the coexistence of multiple chaotic attractors and the coexistence of hyper-chaotic attractors and chaotic attractors in the system. In addition, the system’s complexity is analyzed. It is found that the complexity is close to 1 in the hyper-chaotic state and a pseudo-random sequence generated by the system passes all the statistical tests. Finally, an analog circuit of the system is designed and simulated. © 2020, Shanghai Jiao Tong University and Springer-Verlag GmbH Germany, part of Springer Nature.