J Shanghai Jiaotong Univ Sci ›› 2020, Vol. 25 ›› Issue (5): 639-649.doi: 10.1007/s12204-020-2224-x

• • 上一篇    下一篇

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

XU Changbiao (徐昌彪), WU Xia (吴霞), HE Yinghui (何颖辉), MO Yunhui (莫运辉)    

  1. (a. School of Communication and Information Engineering; b. School of Optoelectronic Engineering, Chongqing University
    of Posts and Telecommunications, Chongqing 400065, China)
  • 出版日期:2020-10-28 发布日期:2020-09-11
  • 通讯作者: WU Xia (吴霞) E-mail:wuxiau@outlook.com

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

XU Changbiao (徐昌彪), WU Xia (吴霞), HE Yinghui (何颖辉), MO Yunhui (莫运辉)    

  1. (a. School of Communication and Information Engineering; b. School of Optoelectronic Engineering, Chongqing University
    of Posts and Telecommunications, Chongqing 400065, China)
  • Online:2020-10-28 Published:2020-09-11
  • Contact: WU Xia (吴霞) E-mail:wuxiau@outlook.com

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

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

中图分类号: