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.

相位减少方法已在分析极限循环振荡器的节律行为中表现出了强大的功能。对于纯粹由噪声引起的相干振荡，例如相干谐振振荡器，随机动力学表现出几乎确定性的极限循环现象，这激发了将相减法应用于此类系统。在本文中，相干共振中的FitzHugh-Nagumo系统被建模为跳跃过程。通过将相减方法应用于混合动力系统可获得相敏度。提出了一种改进的直接方法，将理论结果与随机系统的蒙特卡洛模拟结果进行了比较，表明在扰动不小的情况下具有较好的一致性。相干振荡器的相位降低结果被应用于两个耦合的FitzHugh-Nagumo神经元。有趣的是，耦合相干振荡器的相位差不会像确定性振荡器那样收敛，而是形成一个分布，其中的峰和谷对应于由相位耦合函数预测的稳定和不稳定同步。本文中的思想可以应用于随机动力学遵循确定性路径的其他相干振荡器。