Limit points and Hopf bifurcation points for a one - parameter dynamical system associated to the Luo - Rudy I model

TL;DR

This paper develops algorithms to identify limit points and Hopf bifurcation points in a one-parameter dynamical system modeling cardiac cell excitability, providing numerical bifurcation diagrams for analysis.

Contribution

It introduces new algorithms for locating bifurcation points in a model of cardiac cell dynamics, enhancing understanding of excitability behavior.

Findings

Successful construction of equilibrium curves.

Effective identification of limit points and Hopf bifurcation points.

Numerical bifurcation diagrams illustrating system behavior.

Abstract

A 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. An algorithm used to construct the equilibrium curve is presented. Some test functions are used in order to locate limit points and Hopf bifurcation points. Two extended systems allow to calculate these points. The numerical results are presented in a bifurcation diagram.