Phase sensitivity for coherence resonance oscillators

Abstract

The phase reduction approach has manifested its power in analyzing the rhythmic behaviors for limit cycle oscillators. For coherent oscillation purely induced by noise, e.g., the coherence resonance oscillator, the stochastic dynamics exhibit almost deterministic limit cycle phenomenon which inspires the application of the phase reduction approach to this kind of systems. In this paper, the FitzHugh–Nagumo system in coherence resonance is modeled as a jump process. The phase sensitivity is obtained by applying the phase reduction approach for the hybrid system. A modified direct method is proposed to compare the theoretical results with those of Monte Carlo simulation for the stochastic system, which shows a relatively good agreement for the perturbation not being too small. The phase reduction results of the coherent oscillators are applied to two coupled FitzHugh–Nagumo neurons. It is interesting that the phase difference of the coupled coherent oscillators does not converge as the deterministic oscillators, but forms a distribution where the peaks and valleys correspond to the stable and unstable synchronizations predicted by the phase coupling functions. The idea in this paper could be applied to other coherent oscillators where the stochastic dynamics follow almost deterministic paths.