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Journal Article

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

MPS-Authors

Arai,  Kensuke
Max Planck Society;

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Nakao,  Hiroya
Physical Chemistry, Fritz Haber Institute, Max Planck Society;

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Citation

Arai, K., & Nakao, H. (2008). Averaging approach to phase coherence of uncoupled limit-cycle oscillators receiving common random impulses. Physical Review E, 78(6): 066220. doi:10.1103/PhysRevE.78.066220.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0010-FB41-B
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 differences 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.