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

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

2009-03-12

arxiv.org/abs/0903.2112v1

Phys. Rev. E 78, 066220 (2008)

Nonlinear Sciences

Adaptation and Self-Organizing Systems

Scientific paper

10.1103/PhysRevE.78.066220

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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