耦合方式与初始条件结构对分数阶双稳态振子环形网络同步的影响

王立明; 吴峰

doi:10.7498/aps.63.050503

摘要

在由分数阶双稳态振子通过最近邻耦合构成的环形网络中研究了振子的同步与耦合方式以及初始条件结构的关系. 通过选择初始条件结构、耦合方式和强度，可以控制网络呈现振幅死亡同步态、振幅死亡非同步态、混沌同步态和混沌非同步态等多种动力学行为. 参数平面区域3-2内的最大条件Lyapunov 指数和最大Lyapunov指数的等高线进一步表明，y与z方向的耦合竞争对网络的动力学行为的影响结果敏感地依赖于网络的初始条件结构.

关键词:

初始条件 /
振幅死亡 /
双稳态

Abstract

A ring network with fractional-order bistable oscillators is proposed, and the relationship between synchronization and parameters, such as coupling modes and the initial structural conditions, etc., is investigated. Based on the bistable characteristics of P-R oscillator, the effects of the coupling strength and the structures in initial conditions on the dynamic behaviors of the ring network are investigated by analyzing the largest conditional Lyapunov exponents, the largest Lyapunov exponents and the bifurcation diagrams, etc. Further investigation reveals that the ring network can be controlled to form chaotic synchronization, chaotic non-synchronization, synchronous amplitude death, synchronous non-amplitude death, etc. by changing the initial conditions and the coupling strength. Furthermore, the contours of the largest conditional Lyapunov exponents and the largest Lyapunov exponents also show how the dynamic behaviors of the network are influenced by the competition between couplings along directions of y and z, strongly relies on the initial structural conditions of network.

Keywords:

作者及机构信息

王立明¹,
吴峰²

1.
廊坊师范学院物理系, 廊坊 065000;

2.
天津理工大学理学院, 天津 300191

基金项目: 廊坊师范学院基金（批准号：K2012-08和LSZY201204）和国家自然科学青年基金（批准号：11204214）资助的课题.

Authors and contacts

Wang Li-Ming¹,
Wu Feng²

1.
Department of physics, Langfang Teachers College, Langfang 065000, China;

2.
Department of Physics, Tianjin University of Technology, Tianjin 300191, China

Funds: Project supported by the Langfang Teachers College Foundation, China (Grant Nos. K2012-08 and LSZY201204), and the National Science Fund for Distinguished Young Scholars of China (Grant No. 11204214).

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施引文献

[1]	Lai Y C, Bollt E M, Liu Z H 2003 Chaos Solitons and Fractals 15 219
[2]
[3]	Zhang R X, Yang S P 2009 Acta Phys. Sin. 58 2957 (in Chinese) 张若洵, 杨世平 2009 物理学报 58 2957]
[4]
[5]	Hasler M 1998 Int. J. Bifurcat. Chaos 8 647
[6]
[7]	Heagy J F, Pecora L M, Carroll T L 1995 Phys. Rev. Lett. 74 4185
[8]
[9]	Liu W Q, Qian X L, Yang J Z, Xiao J H 2006 Phys. Lett. A 354 119
[10]
[11]	Yamaguchi Y, Shimizu H 1984 Phycica D 11 212
[12]	Yang J 2007 Phys. Rev. E 76 016204
[13]
[14]	Liu W Q, Xiao J H, Yang J Z 2005 Phys. Rev. E 72 057201
[15]
[16]	Prasad A 2005 Phy. Rev. E 72 056204
[17]
[18]
[19]	Zhu Y, Qian X L, Yang J Z 2008 Europhys. Lett. 82 40001
[20]	Mandelbrot B B 1983 The Fractal Geometiy of Nature (San Diego: W H Freeman Co)
[21]
[22]	Shao S Y, Min F H, Ma M L, Wang E R 2013 Acta Phys. Sin. 62 130504 (in Chinese) [邵书义, 闵富红, 马美玲, 王恩荣 2013 物理学报 62 130504]
[23]
[24]	Jia H Y, Chen Z Q, Xue W 2013 Acta Phys. Sin. 62 140503 (in Chinese) [贾红艳, 陈增强, 薛薇 2013 物理学报 62 140503]
[25]
[26]	Shao S Q, Gao X, Liu X W 2007 Acta Phys. Sin. 56 6815 (in chinese) [邵仕泉, 高心, 刘兴文 2007 物理学报 56 6815]
[27]
[28]
[29]	Deng W H, Li C P 2005 Physica A 353 61
[30]
[31]	Chen X R, Liu C X, Wang F Q, Li Y X 2008 Acta Phys. Sin. 57 1416 (in Chinese) [陈向荣, 刘崇新, 王发强, 李永勋 2008 物理学报 57 1416]
[32]
[33]	Yang S P, Zhang R X 2011 Chin. Phys. B 20 110506
[34]	Gao X, Yu J B 2005 Chaos, Solitons and Fractals 26 141
[35]
[36]	Wang L M, Wu F 2013 Acta Phys. Sin. 62 210504 (in Chinese) [王立明, 吴峰 2013 物理学报 62 210504]
[37]
[38]	Podlubny I 1999 Fractional Differential Equations (Vol. 198) (San Diego: Academic Press) p78
[39]
[40]	Pikovsky A S, Rabinovich M I 1978 Sov. Phys. Dokl. 23 183
[41]
[42]	Li C P, Peng G J 2004 Chaos, Solitons and Fractals 22 443
[43]

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