Qualitative analysis of a mathematical model of calcium dynamics inside the muscle cell

Abstract

In this paper, we consider a mathematical model of calcium dynamics inside the muscle cell, proposed by Williams. We make a qualitative study of the model solutions. In particular, we study the existence and stability of equilibrium points of the model with respect to the model parameters in two limiting cases-when a constant stimulus is present and when there is no stimulus that triggers muscle activity. Numerical examples are given for each case, in order to illustrate the analytic results.