Effects of Reduced Frequency on Network Configuration and Synchronization Transition

doi:10.1088/0256-307X/33/5/050501

Chin. Phys. Lett.

2016, Vol. 33

Issue (05): 050501 DOI: 10.1088/0256-307X/33/5/050501

GENERAL

Effects of Reduced Frequency on Network Configuration and Synchronization Transition

Liu-Hua Zhu^**

Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, College of Physics Science and Engineering Technology, Yulin Normal University, Yulin 537000

Cite this article:

Liu-Hua Zhu 2016 Chin. Phys. Lett. 33 050501

Download: PDF(3882KB) PDF(mobile)(KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract Synchronization of networked phase oscillators depends essentially on the correlation between the topological structure of the graph and the dynamical property of the elements. We propose the concept of 'reduced frequency', a measure which can quantify natural frequencies of each pair of oscillators. Then we introduce an evolving network whose linking rules are controlled by its own dynamical property. The simulation results indicate that when the linking probability positively correlates with the reduced frequency, the network undergoes a first-order phase transition. Meanwhile, we discuss the circumstance under which an explosive synchronization can be ignited. The numerical results show that the peculiar butterfly shape correlation between frequencies and degrees of the nodes contributes to an explosive synchronization transition.

Received: 30 November 2015 Published: 31 May 2016

PACS:	05.45.Xt	(Synchronization; coupled oscillators)
	89.75.Hc	(Networks and genealogical trees)
	89.75.Kd	(Patterns)

TRENDMD:

URL:

https://cpl.iphy.ac.cn/10.1088/0256-307X/33/5/050501 OR https://cpl.iphy.ac.cn/Y2016/V33/I05/050501

Service
	E-mail this article
	E-mail Alert
	RSS
Articles by authors
	Liu-Hua Zhu

[1]	Strogatz S H 2001 Nature 410 268
[2]	Boccaletti S et al 2006 Phys. Rep. 424 175
[3]	Dorogovtsev S N et al 2008 Rev. Mod. Phys. 80 1275
[4]	Gómez-Garde?es J et al 2007 Phys. Rev. E 75 066106
[5]	Leyva I et al 2013 Sci. Rep. 3 1281
[6]	Peron T K D and Rodrigues F A 2012 Phys. Rev. E 86 016102
[7]	Ji P et al 2013 Phys. Rev. Lett. 110 218701
[8]	Chen H S et al 2013 Chaos 23 033124
[9]	Thomas K D P and Francisco A R 2012 Phys. Rev. E 86 056108
[10]	Navas A et al 2015 Phys. Rev. E 92 062820
[11]	Leyva I et al 2012 Phys. Rev. Lett. 108 168702
[12]	Leyva I et al 2013 Phys. Rev. E 88 042808
[13]	Liu W Q et al 2013 Europhys. Lett. 101 38002
[14]	Li P et al 2013 Phys. Rev. E 87 042803
[15]	Coutinho B C et al 2013 Phys. Rev. E 87 032106
[16]	Zhang X Y et al 2013 Phys. Rev. E 88 010802
[17]	Zhang X Y et al 2014 Sci. Rep. 4 5200
[18]	Su G F et al 2013 Europhys. Lett. 103 48004
[19]	Skardal P S et al 2013 Europhys. Lett. 101 20001
[20]	Hu X et al 2014 Sci. Rep. 4 7262
[21]	Bi H J et al 2014 Europhys. Lett. 108 50003
[22]	Wu X L and Yang J Z 2014 Chin. Phys. Lett. 31 060507
[23]	Feng Y E et al 2014 Chin. Phys. Lett. 31 080503
[24]	Kuramoto Y 1984 Chemical Oscillations, Waves and Turbulence (Berlin: Springer)
[25]	Pazo D 2005 Phys. Rev. E 72 046211
[26]	Gómez-Gardenes J et al 2011 Phys. Rev. Lett. 106 128701
[27]	Zhu L H et al 2013 Phys. Rev. E 88 042921
[28]	Kuramoto Y and Nishikawa I 1987 J. Stat. Phys. 49 569
[29]	Gómez-Gardenes J et al 2007 Phys. Rev. Lett. 98 034101
[30]	Hong H et al 2013 Phys. Rev. E 87 042105
[31]	Hung Y C et al 2008 Phys. Rev. E 77 016202
[32]	Arenas A et al 2008 Phys. Rep. 469 93
[33]	Liu Z H 2010 Phys. Rev. E 81 016110
[34]	Acebron J A et al 2005 Rev. Mod. Phys. 77 137
[35]	Wu Y et al 2012 Europhys. Lett. 97 40005
[36]	Pinto R S et al 2015 Phys. Rev. E 91 022818
[37]	Zou Y et al 2014 Phys. Rev. Lett. 112 114102
[38]	Zhang X Y et al 2015 Phys. Rev. Lett. 114 038701
[39]	Zhou W C et al 2015 Phys. Rev. E 92 012812

Related articles from Frontiers Journals

[1]	Liang Zhang, Tian Tian, Pu Huang, Shaochun Lin, Jiangfeng Du. Coherent Transfer of Excitation in a Nanomechanical Artificial Lattice[J]. Chin. Phys. Lett., 2020, 37(1): 050501
[2]	Jing-Hui Li. Effect of Network Size on Collective Motion of Mean Field for a Globally Coupled Map with Disorder[J]. Chin. Phys. Lett., 2016, 33(12): 050501
[3]	Nian-Ping Wu, Hong-Yan Cheng, Qiong-Lin Dai, Hai-Hong Li. The Ott–Antonsen Ansatz in Globally Coupled Phase Oscillators[J]. Chin. Phys. Lett., 2016, 33(07): 050501
[4]	Di Yuan, Dong-Qiu Zhao, Yi Xiao, Ying-Xin Zhang. Travelling Wave in the Generalized Kuramoto Model with Inertia[J]. Chin. Phys. Lett., 2016, 33(05): 050501
[5]	ZHANG Ji-Qian, HUANG Shou-Fang, PANG Si-Tao, WANG Mao-Sheng, GAO Sheng. Synchronization in the Uncoupled Neuron System[J]. Chin. Phys. Lett., 2015, 32(12): 050501
[6]	HU Dong, SUN Xian, LI Ping, CHEN Yan, ZHANG Jie. Factors That Affect the Centrality Controllability of Scale-Free Networks[J]. Chin. Phys. Lett., 2015, 32(12): 050501
[7]	SONG Xin-Fang, WANG Wen-Yuan. Target Inactivation and Recovery in Two-Layer Networks[J]. Chin. Phys. Lett., 2015, 32(11): 050501
[8]	LIU Yu-Long, YU Xiao-Ming, HAO Yu-Hua. Analytical Results for Frequency-Weighted Kuramoto-Oscillator Networks[J]. Chin. Phys. Lett., 2015, 32(11): 050501
[9]	FENG Yue-E, LI Hai-Hong. The Dependence of Chimera States on Initial Conditions[J]. Chin. Phys. Lett., 2015, 32(06): 050501
[10]	HAN Fang, WANG Zhi-Jie, FAN Hong, GONG Tao. Robust Synchronization in an E/I Network with Medium Synaptic Delay and High Level of Heterogeneity[J]. Chin. Phys. Lett., 2015, 32(4): 050501
[11]	JU Ping, YANG Jun-Zhong. Synchronization Dynamics in a System of Multiple Interacting Populations of Phase Oscillators[J]. Chin. Phys. Lett., 2015, 32(03): 050501
[12]	YANG Yan-Jin, DU Ru-Hai, WANG Sheng-Jun, JIN Tao, QU Shi-Xian. Change of State of a Dynamical Unit in the Transition of Coherence[J]. Chin. Phys. Lett., 2015, 32(01): 050501
[13]	G. Sivaganesh. An Analytical Study on the Synchronization of Murali–Lakshmanan–Chua Circuits[J]. Chin. Phys. Lett., 2015, 32(01): 050501
[14]	ZOU Ying-Ying, LI Hai-Hong. Paths to Synchronization on Complex Networks with External Drive[J]. Chin. Phys. Lett., 2014, 31(10): 050501
[15]	FENG Yue-E, LI Hai-Hong, YANG Jun-Zhong. Dynamics of the Kuramoto Model with Bimodal Frequency Distribution on Complex Networks[J]. Chin. Phys. Lett., 2014, 31(08): 050501

Viewed

Full text

Abstract