Synchronization in small-world networks

Ye Wu, Yun Shang, Maoyin Chen, Changsong Zhou, Juergen Kurths

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

In the past decade, synchronization in complex networks, especially the question of synchronizability, attracts a lot of interest. The works on synchronizability in networks with a given topology can be divided into two classes according to the coupling matrix in networks. One is the static mechanism, where the coupling matrix remains fixed during the transition to synchronization. From the degree and load based weighted networks, the synchronizability becomes optimal when the intensities of all oscillators become uniform. The other one is the dynamical mechanism, where the coupling matrix evolves in time by introducing adaptive strengths between connected oscillators. The adaption process can enhance synchronization by modifying the coupling matrix in networks, but the synchronizability is still far from being optimal. This is because the resulting networks have nonuniform intensities even for networks with homogeneous degrees. In this paper we consider complete synchronization in smallworld networks of identical Rossler oscillators by applying a simple but effective dynamical optimization coupling scheme. We realize complete synchronization in networks with undelayed or delayed couplings, as well as ensure that all oscillators have uniform intensities during the transition to synchronization. Moreover, we obtain the coupling matrix with much better synchronizability in a certain range of the probability p for adding longrange connections.

Original languageEnglish
Article number037111
Number of pages7
JournalChaos
Volume18
Issue number3
DOIs
Publication statusPublished - Sep 2008

Cite this

Wu, Y., Shang, Y., Chen, M., Zhou, C., & Kurths, J. (2008). Synchronization in small-world networks. Chaos, 18(3), [037111]. https://doi.org/10.1063/1.2939136

Synchronization in small-world networks. / Wu, Ye; Shang, Yun; Chen, Maoyin; Zhou, Changsong; Kurths, Juergen.

In: Chaos, Vol. 18, No. 3, 037111, 09.2008.

Research output: Contribution to journalArticle

Wu, Y, Shang, Y, Chen, M, Zhou, C & Kurths, J 2008, 'Synchronization in small-world networks', Chaos, vol. 18, no. 3, 037111. https://doi.org/10.1063/1.2939136
Wu Y, Shang Y, Chen M, Zhou C, Kurths J. Synchronization in small-world networks. Chaos. 2008 Sep;18(3). 037111. https://doi.org/10.1063/1.2939136
Wu, Ye ; Shang, Yun ; Chen, Maoyin ; Zhou, Changsong ; Kurths, Juergen. / Synchronization in small-world networks. In: Chaos. 2008 ; Vol. 18, No. 3.
@article{1e4fc49edf324cc8b0c405bafa300cd4,
title = "Synchronization in small-world networks",
abstract = "In the past decade, synchronization in complex networks, especially the question of synchronizability, attracts a lot of interest. The works on synchronizability in networks with a given topology can be divided into two classes according to the coupling matrix in networks. One is the static mechanism, where the coupling matrix remains fixed during the transition to synchronization. From the degree and load based weighted networks, the synchronizability becomes optimal when the intensities of all oscillators become uniform. The other one is the dynamical mechanism, where the coupling matrix evolves in time by introducing adaptive strengths between connected oscillators. The adaption process can enhance synchronization by modifying the coupling matrix in networks, but the synchronizability is still far from being optimal. This is because the resulting networks have nonuniform intensities even for networks with homogeneous degrees. In this paper we consider complete synchronization in smallworld networks of identical Rossler oscillators by applying a simple but effective dynamical optimization coupling scheme. We realize complete synchronization in networks with undelayed or delayed couplings, as well as ensure that all oscillators have uniform intensities during the transition to synchronization. Moreover, we obtain the coupling matrix with much better synchronizability in a certain range of the probability p for adding longrange connections.",
author = "Ye Wu and Yun Shang and Maoyin Chen and Changsong Zhou and Juergen Kurths",
year = "2008",
month = "9",
doi = "10.1063/1.2939136",
language = "English",
volume = "18",
journal = "Chaos",
issn = "1054-1500",
publisher = "American Institute of Physics",
number = "3",

}

TY - JOUR

T1 - Synchronization in small-world networks

AU - Wu, Ye

AU - Shang, Yun

AU - Chen, Maoyin

AU - Zhou, Changsong

AU - Kurths, Juergen

PY - 2008/9

Y1 - 2008/9

N2 - In the past decade, synchronization in complex networks, especially the question of synchronizability, attracts a lot of interest. The works on synchronizability in networks with a given topology can be divided into two classes according to the coupling matrix in networks. One is the static mechanism, where the coupling matrix remains fixed during the transition to synchronization. From the degree and load based weighted networks, the synchronizability becomes optimal when the intensities of all oscillators become uniform. The other one is the dynamical mechanism, where the coupling matrix evolves in time by introducing adaptive strengths between connected oscillators. The adaption process can enhance synchronization by modifying the coupling matrix in networks, but the synchronizability is still far from being optimal. This is because the resulting networks have nonuniform intensities even for networks with homogeneous degrees. In this paper we consider complete synchronization in smallworld networks of identical Rossler oscillators by applying a simple but effective dynamical optimization coupling scheme. We realize complete synchronization in networks with undelayed or delayed couplings, as well as ensure that all oscillators have uniform intensities during the transition to synchronization. Moreover, we obtain the coupling matrix with much better synchronizability in a certain range of the probability p for adding longrange connections.

AB - In the past decade, synchronization in complex networks, especially the question of synchronizability, attracts a lot of interest. The works on synchronizability in networks with a given topology can be divided into two classes according to the coupling matrix in networks. One is the static mechanism, where the coupling matrix remains fixed during the transition to synchronization. From the degree and load based weighted networks, the synchronizability becomes optimal when the intensities of all oscillators become uniform. The other one is the dynamical mechanism, where the coupling matrix evolves in time by introducing adaptive strengths between connected oscillators. The adaption process can enhance synchronization by modifying the coupling matrix in networks, but the synchronizability is still far from being optimal. This is because the resulting networks have nonuniform intensities even for networks with homogeneous degrees. In this paper we consider complete synchronization in smallworld networks of identical Rossler oscillators by applying a simple but effective dynamical optimization coupling scheme. We realize complete synchronization in networks with undelayed or delayed couplings, as well as ensure that all oscillators have uniform intensities during the transition to synchronization. Moreover, we obtain the coupling matrix with much better synchronizability in a certain range of the probability p for adding longrange connections.

U2 - 10.1063/1.2939136

DO - 10.1063/1.2939136

M3 - Article

VL - 18

JO - Chaos

JF - Chaos

SN - 1054-1500

IS - 3

M1 - 037111

ER -