Bifurcations and pattern formation in a generalized Lengyel–Epstein reaction–diffusion model. (March 2020)

• Record Type: Journal Article
• Authors: Mansouri, Djamel; Abdelmalek, Salem; Bendoukha, Samir
• Is Part Of: Chaos, solitons and fractals. Volume 132(2020)
• Publication Date: 2020-03
• Subjects: General lengyel–Epstein model -- Reaction–diffusion -- Hopf–bifurcation -- Pattern formation; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2019.109579
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: This paper investigates the formation of spatial patterns in a general reaction-diffusion system based on the Lengyel-Epstein CIMA model. The existence of non-constant steady state solutions leading to Turing instability is established by means of classical methods. The existence of periodic solutions is established through Hopf bifurcation analysis. Numerical results are presented to illustrate theoretical findings. Abstract: This paper investigates the formation of spatial patterns in a general reaction–diffusion system based on the Lengyel–Epstein CIMA model. By analyzing the properties of the system's unique positive equilibrium in the ODE and PDE cases, we establish the existence of non–constant steady state solutions thereby confirming the existence of Turing instability. Hopf–bifurcation analysis of the system show the existence of periodic solutions in the absence and presence of diffusion. Numerical simulations are presented to validate the theoretical results of the paper.