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Collective Almost Synchronisation in Complex Networks

Author

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

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.

Suggested Citation

  • Murilo S Baptista & Hai-Peng Ren & Johen C M Swarts & Rodrigo Carareto & Henk Nijmeijer & Celso Grebogi, 2012. "Collective Almost Synchronisation in Complex Networks," PLOS ONE, Public Library of Science, vol. 7(11), pages 1-11, November.
    • Handle: RePEc:plo:pone00:0048118
    DOI: 10.1371/journal.pone.0048118
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    References listed on IDEAS

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    1. Dirk Helbing & Illés Farkas & Tamás Vicsek, 2000. "Simulating dynamical features of escape panic," Nature, Nature, vol. 407(6803), pages 487-490, September.
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    1. Ferrari, F.A.S. & Viana, R.L. & Reis, A.S. & Iarosz, K.C. & Caldas, I.L. & Batista, A.M., 2018. "A network of networks model to study phase synchronization using structural connection matrix of human brain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 162-170.

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