New Types of Pattern Formations in a new Reaction-Diffusion Model using Numerical Methods

Pattern formations as mathematical models are grows significantly and the development in subject analysis and the type of mathematical tools offer a wide range in the research aspects. The paper shows results and analysis for a novel reaction-diffusion model, which has unstable features, and satisfy the Turing instability conditions when the diffusion coefficient becomes large enough. Two methods are used to analysis this model, namely semi-implicit finite different method and the analysis Finite element method with utilize of COMSOL Multiphysics software. The conditions of diffusion-driven instability are shown and the effect of diffusion coefficient in changing the state of the model to be unstable is explained. Travelling wave solutions for this model in one dimension are founded and compared using the mentioned two methods. Finally, pattern formations for this model are shown in two dimensions and for different values of diffusion coefficients.