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Seminário Geral: Globally coupled stochastic two-state oscillators: synchronization of infinite and finite arrays

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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 
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.