Adaptive coupling induced multi-stable states in complex networks

V.K. Chandrasekar, Jane H. Sheeba, B. Subash, M. Lakshmanan, J. Kurths

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

Adaptive coupling, where the coupling is dynamical and depends on the behaviour of the oscillators in a complex system, is one of the most crucial factors to control the dynamics and streamline various processes in complex networks. In this paper, we have demonstrated the occurrence of multi-stable states in a system of identical phase oscillators that are dynamically coupled. We find that the multi-stable state is comprised of a two cluster synchronization state where the clusters are in anti-phase relationship with each other and a desynchronization state. We also find that the phase relationship between the oscillators is asymptotically stable irrespective of whether there is synchronization or desynchronization in the system. The time scale of the coupling affects the size of the clusters in the two cluster state. We also investigate the effect of both the coupling asymmetry and plasticity asymmetry on the multi-stable states. In the absence of coupling asymmetry, increasing the plasticity asymmetry causes the system to go from a two clustered state to a desynchronization state and then to a two clustered state. Further, the coupling asymmetry, if present, also affects this transition. We also analytically find the occurrence of the above mentioned multi-stable–desynchronization–multi-stable state transition. A brief discussion on the phase evolution of nonidentical oscillators is also provided. Our analytical results are in good agreement with our numerical observations.
Original languageEnglish
Pages (from-to)36-48
Number of pages13
JournalPhysica. D, Nonlinear Phenomena
Volume267
Early online date5 Sep 2013
DOIs
Publication statusPublished - 15 Jan 2014

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asymmetry
oscillators
plastic properties
synchronism
occurrences
complex systems
causes

Keywords

  • adaptive coupling
  • synchronization
  • complex networks

Cite this

Chandrasekar, V. K., Sheeba, J. H., Subash, B., Lakshmanan, M., & Kurths, J. (2014). Adaptive coupling induced multi-stable states in complex networks. Physica. D, Nonlinear Phenomena, 267, 36-48. https://doi.org/10.1016/j.physd.2013.08.013

Adaptive coupling induced multi-stable states in complex networks. / Chandrasekar, V.K.; Sheeba, Jane H.; Subash, B.; Lakshmanan, M.; Kurths, J.

In: Physica. D, Nonlinear Phenomena, Vol. 267, 15.01.2014, p. 36-48.

Research output: Contribution to journalArticle

Chandrasekar, VK, Sheeba, JH, Subash, B, Lakshmanan, M & Kurths, J 2014, 'Adaptive coupling induced multi-stable states in complex networks', Physica. D, Nonlinear Phenomena, vol. 267, pp. 36-48. https://doi.org/10.1016/j.physd.2013.08.013
Chandrasekar, V.K. ; Sheeba, Jane H. ; Subash, B. ; Lakshmanan, M. ; Kurths, J. / Adaptive coupling induced multi-stable states in complex networks. In: Physica. D, Nonlinear Phenomena. 2014 ; Vol. 267. pp. 36-48.
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