TY - JOUR

T1 - Globally coupled stochastic two-state oscillators

T2 - Synchronization of infinite and finite arrays

AU - Rosas, Alexandre

AU - Escaff, Daniel Elias

AU - Pinto, Italo'Ivo Lima Dias

AU - Lindenberg, Katja

N1 - Publisher Copyright:
© 2016 IOP Publishing Ltd.

PY - 2016/1/21

Y1 - 2016/1/21

N2 - We consider arrays of the simplest two-state (on-off) stochastic units. The units are Markovian, that is, the transitions between the two states occur at a given rate. We construct arrays of N globally coupled binary units, and observe a remarkable richness of behavior as the control parameter that measures the coupling strength is increased. In the mean field limit as we consider the four simplest polynomial forms of coupling that lead to bifurcations, and characterize the associated phase transitions of the arrays. When N is finite there are fluctuations about the well-defined steady states of the infinite arrays. We study the nature of these fluctuations and their effects on the bifurcations in all cases by constructing the appropriate Langevin equations and the associated Fokker-Planck equations.

AB - We consider arrays of the simplest two-state (on-off) stochastic units. The units are Markovian, that is, the transitions between the two states occur at a given rate. We construct arrays of N globally coupled binary units, and observe a remarkable richness of behavior as the control parameter that measures the coupling strength is increased. In the mean field limit as we consider the four simplest polynomial forms of coupling that lead to bifurcations, and characterize the associated phase transitions of the arrays. When N is finite there are fluctuations about the well-defined steady states of the infinite arrays. We study the nature of these fluctuations and their effects on the bifurcations in all cases by constructing the appropriate Langevin equations and the associated Fokker-Planck equations.

KW - coupled arrays

KW - stochastic

KW - synchronization

KW - two-state oscillators

UR - http://www.scopus.com/inward/record.url?scp=84958976007&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/49/9/095001

DO - 10.1088/1751-8113/49/9/095001

M3 - Article

AN - SCOPUS:84958976007

VL - 49

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 9

M1 - 095001

ER -