Stability of Travelling Waves in Electrically Coupled Smooth Muscle Cells

Travelling waves play a vital role in understanding electrical activities in a population of excitable cells, for example, the propagation of signals in neurons. We aim to study the spatiotemporal patterns arising from a reaction-diffusion model of smooth muscle cells. Modulating model parameters, different forms of patterns including propagating pulses and fronts are observed. I will discuss the existence and stability analysis of the travelling waves. The shooting method is considered to approximate the wave speeds of the travelling waves, it turns out that the results are very similar to the wave speeds of the pulse and front solutions estimated from direct simulations of the model. Additionally, the spectral stability of the travelling wave solutions is investigated.