中国物理B ›› 2008, Vol. 17 ›› Issue (7): 2420-2432.doi: 10.1088/1674-1056/17/7/015

• GENERAL • 上一篇    下一篇

Local bifurcation analysis of a four-dimensional hyperchaotic system

吴文娟, 陈增强, 袁著祉   

  1. Department of Automation, Nankai University, Tianjin 300071, China
  • 收稿日期:2007-12-20 修回日期:2008-01-10 出版日期:2008-07-09 发布日期:2008-07-09
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 60774088, 10772135 and 60574036), the Research Foundation from the Ministry of Education of China (Grant Nos 107024 and 207005), the Program for New Century Excellent Talents in University of China (NCET), and the Application Base and Frontier Technology Project of Tianjin, China (Grant No 08JCZDJC21900).

Local bifurcation analysis of a four-dimensional hyperchaotic system

Wu Wen-Juan(吴文娟)†, Chen Zeng-Qiang(陈增强)‡, and Yuan Zhu-Zhi(袁著祉)   

  1. Department of Automation, Nankai University, Tianjin 300071, China
  • Received:2007-12-20 Revised:2008-01-10 Online:2008-07-09 Published:2008-07-09
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 60774088, 10772135 and 60574036), the Research Foundation from the Ministry of Education of China (Grant Nos 107024 and 207005), the Program for New Century Excellent Talents in University of China (NCET), and the Application Base and Frontier Technology Project of Tianjin, China (Grant No 08JCZDJC21900).

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摘要： Local bifurcation phenomena in a four-dimensional continuous hyperchaotic system, which has rich and complex dynamical behaviours, are analysed. The local bifurcations of the system are investigated by utilizing the bifurcation theory and the centre manifold theorem, and thus the conditions of the existence of pitchfork bifurcation and Hopf bifurcation are derived in detail. Numerical simulations are presented to verify the theoretical analysis, and they show some interesting dynamics, including stable periodic orbits emerging from the new fixed points generated by pitchfork bifurcation, coexistence of a stable limit cycle and a chaotic attractor, as well as chaos within quite a wide parameter region.

Abstract: Local bifurcation phenomena in a four-dimensional continuous hyperchaotic system, which has rich and complex dynamical behaviours, are analysed. The local bifurcations of the system are investigated by utilizing the bifurcation theory and the centre manifold theorem, and thus the conditions of the existence of pitchfork bifurcation and Hopf bifurcation are derived in detail. Numerical simulations are presented to verify the theoretical analysis, and they show some interesting dynamics, including stable periodic orbits emerging from the new fixed points generated by pitchfork bifurcation, coexistence of a stable limit cycle and a chaotic attractor, as well as chaos within quite a wide parameter region.

Key words: hyperchaos, pitchfork bifurcation, Hopf bifurcation, centre manifold theorem

中图分类号:  (Numerical simulations of chaotic systems)

  • 05.45.Pq
05.45.Vx (Communication using chaos)