Identification of the FitzHugh–Nagumo Model Dynamics via Deterministic Learning

Abstract

In this paper, a new method is proposed for the identification of the FitzHugh–Nagumo (FHN) model dynamics via deterministic learning. The FHN model is a classic and simple model for studying spiral waves in excitable media, such as the cardiac tissue, biological neural networks. Firstly, the FHN model described by partial differential equations (PDEs) is transformed into a set of ordinary differential equations (ODEs) by using finite difference method. Secondly, the dynamics of the ODEs is identified using the deterministic learning theory. It is shown that, for the spiral waves generated by the FHN model, the dynamics underlying the recurrent trajectory corresponding to any spatial point can be accurately identified by using the proposed approach. Numerical experiments are included to demonstrate the effectiveness of the proposed method.