Existence and Stability Analysis of Periodic Solution of FitzHugh-Nagumo Neuron Model With State-dependent Impulsive Effects

In this paper, a new hybrid neuron model is proposed by combining FitzHugh-Nagumo neuron model with impulsive effect. The properties in the neighborhood of the equilibrium point of the system are qualitatively analyzed. Based on the theory of impulsive semi-dynamical system, the poincaré map is established by using the poincaré section and the geometric theory of ordinary differential equation. Several sufficient conditions for the existence of order-1 periodic solution, order-2 periodic solution and orbital asymptotic stability are obtained. Some simulaton examples are given to demonstrate the correctness of our theory.