Synchronization and fluctuations: Coupling a finite number of stochastic units

Alexandre Rosas, Jaime Cisternas, Daniel Escaff, Italo'Ivo Lima Dias Pinto, Katja Lindenberg

Resultado de la investigación: Contribución a una revistaArtículorevisión exhaustiva

Resumen

It is well established that ensembles of globally coupled stochastic oscillators may exhibit a nonequilibrium phase transition to synchronization in the thermodynamic limit (infinite number of elements). In fact, since the early work of Kuramoto, mean-field theory has been used to analyze this transition. In contrast, work that directly deals with finite arrays is relatively scarce in the context of synchronization. And yet it is worth noting that finite-number effects should be seriously taken into account since, in general, the limits N→∞ (where N is the number of units) and t→∞ (where t is time) do not commute. Mean-field theory implements the particular choice first N→∞ and then t→∞. Here we analyze an ensemble of three-state coupled stochastic units, which has been widely studied in the thermodynamic limit. We formally address the finite-N problem by deducing a Fokker-Planck equation that describes the system. We compute the steady-state solution of this Fokker-Planck equation (that is, finite N but t→∞). We use this steady state to analyze the synchronic properties of the system in the framework of the different order parameters that have been proposed in the literature to study nonequilibrium transitions.
Idioma originalInglés
Número de artículo062140
PublicaciónPhysical Review E
Volumen101
N.º6
DOI
EstadoPublicada - jun 2020

Nota bibliográfica

Publisher Copyright:
© 2020 American Physical Society.

Huella

Profundice en los temas de investigación de 'Synchronization and fluctuations: Coupling a finite number of stochastic units'. En conjunto forman una huella única.

Citar esto