中国物理B ›› 2014, Vol. 23 ›› Issue (5): 50506-050506.doi: 10.1088/1674-1056/23/5/050506

• GENERAL • 上一篇    下一篇

Collective dynamics in a non-dissipative two-coupled pendulum system

陈子辰, 李博, 邱海波, 惠小强   

  1. School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710061, China
  • 收稿日期:2013-08-29 修回日期:2013-10-11 出版日期:2014-05-15 发布日期:2014-05-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11104217, 11174165, and 11275099).

Collective dynamics in a non-dissipative two-coupled pendulum system

Chen Zi-Chen (陈子辰), Li Bo (李博), Qiu Hai-Bo (邱海波), Xi Xiao-Qiang (惠小强)   

  1. School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710061, China
  • Received:2013-08-29 Revised:2013-10-11 Online:2014-05-15 Published:2014-05-15
  • Contact: Qiu Hai-Bo E-mail:phyqiu@gmail.com
  • About author:05.45.Pq; 05.45.Xt; 05.70.Fh
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11104217, 11174165, and 11275099).

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摘要： We study the collective dynamics of a non-dissipative two-coupled pendulum system, including phase synchronization (PS) and measure synchronization (MS). We find that as the coupling intensity between the two pendulums increases, the PS happens prior to the MS. We also present a three-dimensional phase space representation of MS, from which a more detailed information about evolution can be obtained. Furthermore, the order parameters are introduced to describe the phase transition between PS and MS. Finally, through the analysis of the Poincaré sections, we show that the system exhibits separatrix crossing behavior right at the MS transition point, and as the total initial energy increases, the Hamiltonian chaos will arise with separatrix chaos at the chaotic MS transition point.

关键词: two-coupled pendulum system, phase synchronization, measure synchronization, Poincaré, section analysis

Abstract: We study the collective dynamics of a non-dissipative two-coupled pendulum system, including phase synchronization (PS) and measure synchronization (MS). We find that as the coupling intensity between the two pendulums increases, the PS happens prior to the MS. We also present a three-dimensional phase space representation of MS, from which a more detailed information about evolution can be obtained. Furthermore, the order parameters are introduced to describe the phase transition between PS and MS. Finally, through the analysis of the Poincaré sections, we show that the system exhibits separatrix crossing behavior right at the MS transition point, and as the total initial energy increases, the Hamiltonian chaos will arise with separatrix chaos at the chaotic MS transition point.

Key words: two-coupled pendulum system, phase synchronization, measure synchronization, Poincaré, section analysis

中图分类号:  (Numerical simulations of chaotic systems)

  • 05.45.Pq
05.45.Xt (Synchronization; coupled oscillators) 05.70.Fh (Phase transitions: general studies)