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Collective behavior of coupled nonuniform stochastic oscillators

Author

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  • Assis, Vladimir R.V.
  • Copelli, Mauro

Abstract

Theoretical studies of synchronization are usually based on models of coupled phase oscillators which, when isolated, have constant angular frequency. Stochastic discrete versions of these uniform oscillators have also appeared in the literature, with equal transition rates among the states. Here we start from the model recently introduced by Wood et al. [K. Wood, C. Van den Broeck, R. Kawai, K. Lindenberg, Universality of synchrony: critical behavior in a discrete model of stochastic phase-coupled oscillators, Phys. Rev. Lett. 96 (2006) 145701], which has a collectively synchronized phase, and parametrically modify the phase-coupled oscillators to render them (stochastically) nonuniform. We show that, depending on the nonuniformity parameter 0≤α≤1, a mean field analysis predicts the occurrence of several phase transitions. In particular, the phase with collective oscillations is stable for the complete graph only for α≤α′<1. At α=1 the oscillators become excitable elements and the system has an absorbing state. In the excitable regime, no collective oscillations were found in the model.

Suggested Citation

  • Assis, Vladimir R.V. & Copelli, Mauro, 2012. "Collective behavior of coupled nonuniform stochastic oscillators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1900-1906.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:4:p:1900-1906
    DOI: 10.1016/j.physa.2011.10.012
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    References listed on IDEAS

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    1. S. Risau-Gusman & G. Abramson, 2007. "Bounding the quality of stochastic oscillations in population models," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 60(4), pages 515-520, December.
    2. Agnes, E.J. & Erichsen, R. & Brunnet, L.G., 2010. "Synchronization regimes in a map-based model neural network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 651-658.
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    Cited by:

    1. Moy, Tiago & Pinto, Italo’Ivo L.D. & Rosas, Alexandre, 2020. "Finite number fluctuations in a three-state model with growing population," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).

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