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

Kensuke Arai; Hiroya Nakao

doi:10.1103/physreve.77.036218

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arXiv · 0802.3758

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

Kensuke Arai·Hiroya Nakao

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Abstract

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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Kensuke Arai, Hiroya Nakao. 2008-02-26. Phase coherence in an ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses. https://doi.org/10.1103/physreve.77.036218

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