The Travelling Wave Of Gray-Scott Systems–Existence, Multiplicity And Stability

Keywords

Gray-Scott model; multi-peak waves; spreading of local disturbance; stability; travelling wave

Abstract

This article studies existence and stability of travelling wave of unstirred Gray-Scott system in biological pattern formation which models an isothermal chemical reaction A + 2B → 3B involving two chemical species, a reactant A and an auto-catalyst B, and a linear decay B → C, 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 A + 2B → 3B, is also studied.

Publication Date

8-11-2017

Publication Title

Journal of Biological Dynamics

Volume

11

Number of Pages

379-399

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1080/17513758.2017.1308566

Socpus ID

85017256470 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85017256470

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