Averaging approach to phase coherence of uncoupled limit-cycle oscillators receiving common random impulses

Kensuke Arai; Hiroya Nakao

doi:10.1103/physreve.78.066220

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arXiv · 0903.2112

Averaging approach to phase coherence of uncoupled limit-cycle oscillators receiving common random impulses

Kensuke Arai·Hiroya Nakao

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Abstract

Populations of uncoupled limit-cycle oscillators receiving common random impulses show various types of phase-coherent states, which are characterized by the distribution of phase differences between pairs of oscillators. We develop a theory to predict the stationary distribution of pairwise phase difference from the phase response curve, which quantitatively encapsulates the oscillator dynamics, via averaging of the Frobenius-Perron equation describing the impulse-driven oscillators. The validity of our theory is confirmed by direct numerical simulations using the FitzHugh-Nagumo neural oscillator receiving common Poisson impulses as an example.

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Kensuke Arai, Hiroya Nakao. 2009-03-12. Averaging approach to phase coherence of uncoupled limit-cycle oscillators receiving common random impulses. https://doi.org/10.1103/physreve.78.066220

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