中国物理B ›› 2004, Vol. 13 ›› Issue (6): 828-835.doi: 10.1088/1009-1963/13/6/008

• GENERAL • 上一篇    下一篇

The dynamical feature of transition of a Hamiltonian system to a dissipative system

张广才, 张洪钧   

  1. Laboratory of Optical Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100080, China
  • 收稿日期:2003-09-24 修回日期:2004-01-05 出版日期:2005-07-05 发布日期:2005-07-05
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 19835020).

The dynamical feature of transition of a Hamiltonian system to a dissipative system

Zhang Guang-Cai (张广才), Zhang Hong-Jun (张洪钧)   

  1. Laboratory of Optical Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100080, China
  • Received:2003-09-24 Revised:2004-01-05 Online:2005-07-05 Published:2005-07-05
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 19835020).

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摘要： The mechanism of generation and annihilation of attractors during transition from a Hamiltonian system to a dissipative system is studied numerically using the dissipative standard map. The transient process related to the formation of attracting basins of periodic attractors is studied by discussing the evolution of the KAM tori of the standard map. The result shows that as damping increases, attractors are mainly generated from elliptic orbits of the Hamiltonian system and annihilated by colliding with unstable periodic orbits originating from the corresponding hyperbolic orbits of the Hamiltonian system. The transient process also exhibits the general feature of bifurcation.

Abstract: The mechanism of generation and annihilation of attractors during transition from a Hamiltonian system to a dissipative system is studied numerically using the dissipative standard map. The transient process related to the formation of attracting basins of periodic attractors is studied by discussing the evolution of the KAM tori of the standard map. The result shows that as damping increases, attractors are mainly generated from elliptic orbits of the Hamiltonian system and annihilated by colliding with unstable periodic orbits originating from the corresponding hyperbolic orbits of the Hamiltonian system. The transient process also exhibits the general feature of bifurcation.

Key words: dynamic system, dissipative standard map, KAM torus

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a