Singular Perturbation Approach with Matsuoka Oscillator and Synchronization Phenomena

摘要

We study the singular perturbation approach in a pair of Matsuoka nonlinear neural oscillators, which consist of membrane potential (v) and recovery (u) dynamics with a relaxation rate (P). This shows that the u-coupled system of the Matsuoka oscillators would be valid for the modeling of neural firings. The coupled integrate-and-fire model of the improved type with an impulse-like interval results from the u-coupled system, under taking the limit of P → ∞, without loss of any coupling properties. We simulate systematically synchronization of both the v-coupled and u-coupled systems. We also discuss potential capabilities of the u-coupled system of Matsuoka oscillators.