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Chin. Phys. B, 2014, Vol. 23(5): 050506    DOI: 10.1088/1674-1056/23/5/050506
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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)
School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710061, China
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.
Keywords:  two-coupled pendulum system      phase synchronization      measure synchronization      Poincaré      section analysis  
Received:  29 August 2013      Revised:  11 October 2013      Accepted manuscript online: 
PACS:  05.45.Pq (Numerical simulations of chaotic systems)  
  05.45.Xt (Synchronization; coupled oscillators)  
  05.70.Fh (Phase transitions: general studies)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11104217, 11174165, and 11275099).
Corresponding Authors:  Qiu Hai-Bo     E-mail:  phyqiu@gmail.com
About author:  05.45.Pq; 05.45.Xt; 05.70.Fh

Cite this article: 

Chen Zi-Chen (陈子辰), Li Bo (李博), Qiu Hai-Bo (邱海波), Xi Xiao-Qiang (惠小强) Collective dynamics in a non-dissipative two-coupled pendulum system 2014 Chin. Phys. B 23 050506

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