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.
Accepted manuscript online:
PACS:
05.45.-a
(Nonlinear dynamics and chaos)
Fund: 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
Cite this article:
Wu Wen-Juan(吴文娟), Chen Zeng-Qiang(陈增强), and Yuan Zhu-Zhi(袁著祉) Analysis of two-torus in a new four-dimensional autonomous system 2008 Chin. Phys. B 17 129
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