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.
Highlights
Spiral waves are one of the most typical two-dimensional spatiotemporal patterns in excitable or oscillatory reactiondiffusion systems, which can be observed in a variety of chemical and biological systems
In this study, a novel method via deterministic learning and interpolation is proposed for identifying FHN model dynamics
It extends the method proposed in [29] from one-dimensional distributed parameter system (DPS) to a two-dimensional DPS with coupled variables, and achieves the global identification of the FHN model based on system states at a set of spatial points
Summary
Spiral waves are one of the most typical two-dimensional spatiotemporal patterns in excitable or oscillatory reactiondiffusion systems, which can be observed in a variety of chemical and biological systems. The FitzHugh-Nagumo(FHN) model [4], [5], a simplified modification of the famous Hodgkin-Huxley model (the first mathematical model of myocardial cell) [6], has been used as a classic model for decades in the study of spiral waves in excitable media [7], [8]. It is useful for the study of biology, genetics, and heat and mass transfer. It is of great significance to study the dynamics of FHN model in practical application
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