Desynchronization waves in small-world networks

Kwangho Park, Liang Huang, Ying-Cheng Lai

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)

Abstract

A regular array of oscillators with random coupling exhibits a transition from synchronized motion to desynchronized but ordered waves as a global coupling parameter is increased, due to the spread of localized instability of eigenvectors of the Laplacian matrix. We find that shortcuts, which make a regular network small-world, can destroy ordered desynchronization wave patterns. Wave patterns in a small-world network are usually destroyed gradually as the degree of regularity in the network deteriorates. No ordered wave patterns are observed in scale-free and random networks. The formation of ordered wave patterns in a coupled oscillator network can be explained by considering the time evolution of phase in each oscillator. We derive a general type of the Kardar-Parisi-Zhang equation for phase evolution in a prototype oscillator network. The equation demonstrates well the ordered desynchronized wave patterns found in the network with and without shortcuts. Our results provide a qualitative justification for the requirement of certain degree of regularity in the network for ordered wave patterns to arise.

Original languageEnglish
Article number026211
Number of pages5
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume75
Issue number2
DOIs
Publication statusPublished - 21 Feb 2007

Keywords

  • complex networks
  • synchronization
  • interface
  • growth

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