| Analysis of two-torus in a new four-dimensional autonomous system |
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| 作者姓名： | 吴文娟 陈增强 袁著祉 |
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| 作者单位： | Department of Automation, Nankai University, Tianjin
300071, China;Department of Automation, Nankai University, Tianjin
300071, China;Department of Automation, Nankai University, Tianjin
300071, China |
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| 基金项目： | 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-dimenslonal 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.
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| 关 键 词： | 双环面 标准环面 Lyapunov指数 自动系统 |
Analysis of two-torus in a new four-dimensional autonomous system |
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| Wu Wen-Juan,Chen Zeng-Qiang and Yuan Zhu-Zhi.Analysis of two-torus in a new four-dimensional autonomous system[J].Chinese Physics B,2008,17(1):129-134. |
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| Authors: | Wu Wen-Juan Chen Zeng-Qiang and Yuan Zhu-Zhi |
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| Institution: | Department of Automation, Nankai University, Tianjin
300071, China |
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| 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 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. |
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| Keywords: | two-torus two-frequency
quasiperiodicity standard torus Poincar\'{e} section Lyapunov
exponent |
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