Understanding the mechanism of heart dysfunction through modeling and simulation

It is known that the electrical activities in the cardiac cells give rise to periodic action potentials in one dimension. So, in order to understand the heart dysfunction, one needs to study the behavior of periodic signals in the myocardium cells of the heart wall. The propagation of these periodic signals is called periodic traveling waves. This paper study the bifurcation behavior in the periodic waves in a two-component FitzHugh-Nagumo type reaction-diffusion system. We show the existence and stability of the periodic traveling waves in a one-parameter family of solutions. An Eckhaus bifurcation is found to occur between stable and unstable periodic traveling waves. We explain the stability by the numerical calculation of essential spectra of the periodic traveling wave solutions. In two dimensions, it is found that a stable spiral pattern bifurcates to a complicated spatiotemporal pattern in the same computational settings.