Global Identification of FitzHugh-Nagumo Equation via Deterministic Learning and Interpolation

Abstract

Spiral wave is closely related to the occurrence of malignant ventricular arrhythmia. It is important and necessary to study the spiral wave dynamics to better analyze and control spiral waves. In this paper, the dynamics of FitzHugh-Nagumo(FHN) model is identified by using a novel method based on deterministic learning and interpolation method. The FHN model, which has been studied extensively in physical and mathematical science, is often used to study spiral waves. It is a distributed parameter (DPS) described by two coupled partial differential equations (PDEs). To identify the underlying system dynamics of the FHN model globally, we first transform the FHN model into a set of ordinary differential equations (ODEs) by applying the method of lines. Then, we identify the dynamics of the approximation system by employing deterministic learning. That is, the FHN dynamics on a set of spatial grid nodes is accurately identified. To achieve the global identification of the FHN model, the underlying system dynamics of the FHN model on any other spatial point is approximated via an algorithm based on the interpolation method. The effectiveness and feasibility of the proposed method are demonstrated theoretically and numerically.