The travelling wave of Gray-Scott systems - existence, multiplicity and stability

This article studies existence and stability of travelling wave of unstirred Gray-Scott system in biological pattern formation which models an isothermal chemical reaction [Formula: see text] involving two chemical species, a reactant A and an auto-catalyst B, and a linear decay [Formula: see text], where C is an inert product. Our result shows a new and very distinctive feature of Gray-Scott type of models in generating rich and structurally different travelling pulses than related models in the literature. In particular, the existence of multiple travelling waves which have distinctive number of local maxima is proved. Furthermore, the stability of travelling wave of the reaction-diffusion system of isothermal diffusion system [Formula: see text], is also studied.