中国物理B ›› 2006, Vol. 15 ›› Issue (6): 1216-1225.doi: 10.1088/1009-1963/15/6/015

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The generation of a hyperchaotic system based on a three-dimensional autonomous chaotic system

王杰智, 陈增强, 袁著祉   

  1. Department of Automation, Nankai University,Tianjin 300070, China
  • 收稿日期:2006-01-16 修回日期:2006-02-23 出版日期:2006-06-20 发布日期:2006-06-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 60374037 and 60574036), the Specialized Research Fund for the Doctoral Program of China (Grant No 20050055013) and the Program for New Century Excellent Talents in University of China (NCET).

The generation of a hyperchaotic system based on a three-dimensional autonomous chaotic system

Wang Jie-Zhi (王杰智), Chen Zeng-Qiang (陈增强), Yuan Zhu-Zhi (袁著祉)   

  1. Department of Automation, Nankai University,Tianjin 300070, China
  • Received:2006-01-16 Revised:2006-02-23 Online:2006-06-20 Published:2006-06-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 60374037 and 60574036), the Specialized Research Fund for the Doctoral Program of China (Grant No 20050055013) and the Program for New Century Excellent Talents in University of China (NCET).

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摘要： This paper reports a new four-dimensional hyperchaotic system obtained by adding a controller to a three-dimensional autonomous chaotic system. The new system has two parameters, and each equation of the system has one quadratic cross-product term. Some basic properties of the new system are analysed. The different dynamic behaviours of the new system are studied when the system parameter $a$ or $b$ is varied. The system is hyperchaotic in several different regions of the parameter $b$. Especially, the two positive Lyapunov exponents are both larger, and the hyperchaotic region is also larger when this system is hyperchaotic in the case of varying $a$. The hyperchaotic system is analysed by Lyapunov-exponents spectrum, bifurcation diagrams and Poincar\'{e} sections.

关键词: chaos, chaos generation, hyperchaotic system, bifurcation analysis

Abstract: This paper reports a new four-dimensional hyperchaotic system obtained by adding a controller to a three-dimensional autonomous chaotic system. The new system has two parameters, and each equation of the system has one quadratic cross-product term. Some basic properties of the new system are analysed. The different dynamic behaviours of the new system are studied when the system parameter $a$ or $b$ is varied. The system is hyperchaotic in several different regions of the parameter $b$. Especially, the two positive Lyapunov exponents are both larger, and the hyperchaotic region is also larger when this system is hyperchaotic in the case of varying $a$. The hyperchaotic system is analysed by Lyapunov-exponents spectrum, bifurcation diagrams and Poincaré sections.

Key words: chaos, chaos generation, hyperchaotic system, bifurcation analysis

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a