Phase coherence in an ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses

Details Phase coherence in an ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses Phase coherence in an ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses

2008-02-26

arxiv.org/abs/0802.3758v1

PHYSICAL REVIEW E 77, 036218 2008

Nonlinear Sciences

Adaptation and Self-Organizing Systems

Scientific paper

10.1103/PhysRevE.77.036218

An ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses shows a range of non-trivial behavior, from synchronization, desynchronization, to clustering. The group behavior that arises in the ensemble can be predicted from the phase response of a single oscillator to a given impulsive perturbation. We present a theory based on phase reduction of a jump stochastic process describing a Poisson-driven limit-cycle oscillator, and verify the results through numerical simula- tions and electric circuit experiments. We also give a geometrical interpretation of the synchronizing mechanism, a perturbative expansion to the stationary phase distribution, and the diffusion limit of our jump stochastic model.

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