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

作　　者：吴文娟 陈增强 袁著祉 

机构地区：[1]Department of Automation, Nankai University

出　　处：《Chinese Physics B》2008年第1期129-134,共6页中国物理B（英文版）

基　　金：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 China (NCET);the Science and Technology Research Key Project of Education Ministry of China (Grant No 107024)

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.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.

关 键 词：two-torus two-frequency quasiperiodicity standard torus Poincaré section Lyapunov exponent 

分 类 号：O415.3[理学—理论物理]