中国物理B ›› 2008, Vol. 17 ›› Issue (1): 129-134.doi: 10.1088/1674-1056/17/1/023

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Analysis of two-torus in a new four-dimensional autonomous system

吴文娟, 陈增强, 袁著祉   

  1. Department of Automation, Nankai University, Tianjin 300071, China
  • 出版日期:2008-01-20 发布日期:2008-01-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 60774088 and 60574036), the Specialized Research Fund for the Doctoral Program of China (Grant No 20050055013), the Program for New Century Excellent Talents in University of

Analysis of two-torus in a new four-dimensional autonomous 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
  • Online:2008-01-20 Published:2008-01-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 60774088 and 60574036), the Specialized Research Fund for the Doctoral Program of China (Grant No 20050055013), the Program for New Century Excellent Talents in University of

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摘要： In this paper, we report the dynamical behaviours of a four-dimensional autonomous continuous dissipative system analysed when the parameter is varied in the range we are interested in. The system changes its dynamical modes between periodic motion and quasiperiodic motion. Furthermore, the existence of two-torus is investigated numerically by means of Lyapunov exponents. By taking advantage of phase portraits and Poincar\'{e} sections, two types of the two-torus are observed and proved to have the structure of ring torus and horn torus, both of which are known to be the standard tori.

关键词: two-torus, two-frequency quasiperiodicity, standard torus, Poincar\'{e} section, Lyapunov exponent

Abstract: In this paper, we report the dynamical behaviours of a four-dimensional autonomous continuous dissipative system analysed when the parameter is varied in the range we are interested in. The system changes its dynamical modes between periodic motion and quasiperiodic motion. Furthermore, the existence of two-torus is investigated numerically by means of Lyapunov exponents. By taking advantage of phase portraits and Poincaré sections, two types of the two-torus are observed and proved to have the structure of ring torus and horn torus, both of which are known to be the standard tori.

Key words: two-torus, two-frequency quasiperiodicity, standard torus, Poincaré section, Lyapunov exponent

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a