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

doi:10.1088/1674-1056/23/5/050506

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

[1]	Dlião R 2009 Chaos 19 023118
[2]	Czołczyński K, Perlikowski P, Stefański A, and Kapitaniak T 2011 Int. J. Bifurcat. Chaos 21 2047
[3]	Czołczyński K, Perlikowski P, Stefański A, and Kapitaniak T 2011 Chaos 21 023129
[4]	Huynh H N and Chew L Y 2010 Int. J. Bifurcat. Chaos 20 2427
[5]	Hampton A and Zanette D H 1999 Phys. Rev. Lett. 83 2179
[6]	Chen S Y, Xu H B, Wang G R and Chen S G 2004 Acta Phys. Sin. 53 4098 (in Chinese)
[7]	Wang X G, Zhan M, Lai C H and Hu G 2003 Phys. Rev. E 67 066215
[8]	Wang X G, Zhang Y and Hu G 2002 Phys. Lett. A 298 383
[9]	Vincent U E 2005 New J. Phys 7 209
[10]	Yang Y, Wang C L, Jiang H, Chen J M and Duan W S 2012 Phys. Scr. 86 015003
[11]	Zhang J R, Jiang H, Yang Y, Duan W S and Chen J M 2012 Phys. Scr. 86 065602
[12]	Qiu H B, Tian J and Fu L B 2010 Phys. Rev. A 81 043613
[13]	Tian J, Qiu H B, Wang G F, Chen Y and Fu L B 2013 Phys. Rev. E 88 032906
[14]	Tian J, Qiu H B, Chen Z C and Chen Y 2013 Mod. Phys. Lett. B 27 1350036

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