Limit cycles by FEM for a one-parameter dynamical system associated to the Luo-Rudy I model

TL;DR

This paper applies finite element methods combined with continuation techniques to numerically approximate limit cycles in a one-parameter model of cardiac cell excitability, starting from a Hopf bifurcation point.

Contribution

It introduces a FEM-based approach to compute limit cycles in a cardiac cell model, integrating arc-length continuation and Newton's method for improved numerical analysis.

Findings

Successful computation of limit cycles from bifurcation points

Numerical results demonstrating the method's effectiveness

Application to a cardiac cell excitability model

Abstract

An one-parameter dynamical system is associated to the mathematical problem governing the membrane excitability of a ventricular cardiomyocyte, according to the Luo-Rudy I model. Limit cycles are described by the solutions of an extended system. A finite element method time approximation (FEM) is used in order to formulate the approximate problem. Starting from a Hopf bifurcation point, approximate limit cycles are obtained, step by step, using an arc-length-continuation method and Newton's method. Some numerical results are presented.