Collective almost synchronisation in complex networks

Murilo S Baptista, Hai-Peng Ren, Johen C M Swarts, Rodrigo Carareto, Henk Nijmeijer, Celso Grebogi

Research output: Contribution to journalArticle

12 Citations (Scopus)
3 Downloads (Pure)

Abstract

This work introduces the phenomenon of Collective Almost Synchronisation (CAS), which describes a universal way of how patterns can appear in complex networks for small coupling strengths. The CAS phenomenon appears due to the existence of an approximately constant local mean field and is characterised by having nodes with trajectories evolving around periodic stable orbits. Common notion based on statistical knowledge would lead one to interpret the appearance of a local constant mean field as a consequence of the fact that the behaviour of each node is not correlated to the behaviours of the others. Contrary to this common notion, we show that various well known weaker forms of synchronisation (almost, time-lag, phase synchronisation, and generalised synchronisation) appear as a result of the onset of an almost constant local mean field. If the memory is formed in a brain by minimising the coupling strength among neurons and maximising the number of possible patterns, then the CAS phenomenon is a plausible explanation for it.

Original languageEnglish
Article numbere48118
Number of pages11
JournalPloS ONE
Volume7
Issue number11
DOIs
Publication statusPublished - 8 Nov 2012

Keywords

  • chaos
  • systems
  • transition
  • generalized synchronization
  • phase
  • behavior

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