Spatio-temporal Brusselator Model and Biological Pattern Formation
Zakir Hossine
Department of Applied Mathematics, University of Dhaka, Dhaka 1000, Bangladesh
Oishi Khanam
Department of Applied Mathematics, University of Dhaka, Dhaka 1000, Bangladesh.
Md. Mashih Ibn Yasin Adan
Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh.
Md. Kamrujjaman *
Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh and Department of Mathematics and Statistics, University of Calgary, Calgary, AB, Canada
*Author to whom correspondence should be addressed.
Abstract
This paper explores a two-species non-homogeneous reaction-diffusion model for the study of pattern formation with the Brusselator model. We scrutinize the pattern formation with initial conditions and Neumann boundary conditions in a spatially heterogeneous environment. In the whole investigation, we assume the case for random diffusion strategy. The dynamics of model behaviors show that the nature of pattern formation with varying parameters and initial conditions thoroughly. The model also studies in the absence of diffusion terms. The theoretical and numerical observations explain pattern formation using the reaction-diffusion model in both one and two dimensions.
Keywords: Pattern formation, turing pattern, reaction-diffusion, numerical analysis