Collective behavior of coupled nonuniform stochastic oscillators |
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Authors: | Vladimir RV Assis Mauro Copelli |
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Institution: | a Departamento de Física, Universidade Estadual de Feira de Santana, 44031-460, Feira de Santana, Bahia, Brazilb Centro Brasileiro de Pesquisas Físicas, R. Dr. Xavier Sigaud, 150, 22290-180 Rio de Janeiro-RJ, Brazilc Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, PE, Brazil |
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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. |
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Keywords: | Synchronization Nonequilibrium phase transitions Nonlinear dynamics Excitable media |
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