Transition of spiral solutions according to the time and space steps discretization of reaction-diffusion system of FitzHugh-Nagumo type

Abstract

Spiral solutions or spiral waves can be found in many natural systems. Spiral waves were observed in studies about the potential in brain and heart cells. Their appearance in the human heart is a presentation of arrhythmia. The paper showed how to create spiral solutions of diffusion-reaction system of FitzHugh-Nagumo type and the transition of spiral solutions according to the time step and space step discretization of finite difference method. Decreasing the value of space step discretization makes the spiral wave grow bigger, but if the value of time step discretization is increased at the same given space step, the finite difference method will be explosive, meaning that spiral wave no longer exists.