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

doi:10.1007/s12204-020-2224-x

Abstract

Abstract: 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 hyperbolictype
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.

Key words: hyper-chaos| equilibrium point| multi-stability| pseudorandom sequence| chaotic circuit

摘要： 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 hyperbolictype
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.

关键词: hyper-chaos| equilibrium point| multi-stability| pseudorandom sequence| chaotic circuit

CLC Number:

TP 273

XU Changbiao, WU Xia, HE Yinghui, MO Yunhui . 5D Hyper-Chaotic System with Multiple Types of Equilibrium Points[J]. J Shanghai Jiaotong Univ Sci, 2020, 25(5): 639-649.

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