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Collective behavior of a nearest neighbor coupled system in a dichotomous fluctuating potential. (English) Zbl 07274902
Summary: In this study, the collective and stochastic resonance (SR) behavior of a stochastic nearest neighbor coupled system in a dichotomous fluctuating potential driven by a periodic force are investigated. The exact conditions of stability, synchronization and SR of the system are given analytically and verified by a numerical algorithm. We find that the final dynamic behaviors of the system are the results of the synergy of the coupled system, noise and external periodic force: the stationary regime criterion is only related to the noise parameters and system potential parameter; the synchronization criterion is related to the number of particles, coupling strength, noise parameters and system potential parameter. Furthermore, for the stationary regime, all particles synchronously move with their mean field and show SR phenomenon. For the non-stationary regime, the power-law distribution is observed when the synchronization criteria is satisfied.
##### MSC:
 82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
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