Bifurcation analysis of periodic action potentials of cardiac excitation in the Aliev-Panfilov model

Abstract

Aliev-Panfilov model is a well-known and well-studied model to understand cardiac excitation. In this paper, we consider the Aliev-Panfilov reaction-diffusion system of PDE to understand the mechanism of ventricular fibrillation. It is known that the electrical activities of the heart cells create action potentials periodically. That is why we study the bifurcation analysis of periodic traveling waves (PTWs). We also determine the locus of solutions where the stable waves change their behavior. A stability change of Eckhaus type is observed in our outcomes. We compute the essential spectrum of the waves to comprehend these phenomena.