Patern Formation and Diffusion-Driven Instability of a Modified Lengyel-Epstein Model

Abstract

We consider a modified Lengyel-Epstein model that is covered by a system of reaction diffusion equations and investigate the sufficient conditions on parameters of the model at which the diffusion driven instability occurs. We perform numerical simulations to support and extend the theoretical findings. Analytical results and numerical simulations show that the modified Lengyel-Epstein system with positive initial and non-flux boundary conditions presents Turing patterns under some conditions on its parameters. Lengyel–Epstein system 2008 MSC: 35K57, 35K50, 92D25, 92C15 (2000 is the default)