Two dimension spatial pattern formation in a coupled autocatalysis system

This paper addresses the cubic autocatalator kinetics modeling of coupling via diffusion interchange of autocatalyst. By incorporating the effect of two identical cells, each governed by cubic autocatalator kinetics, considering the possibility of the spatiotemporal structures of two dimensional Turing patterns, a new model is proposed. Unlike previous models, the proposed model has two dimensional spatial variation. First, the equations and the local stability are obtained by linearizing about the spatially uniform solutions. It is shown that the necessary condition for the model undergoes bifurcation by using the singular perturbation theory. Next Landau constant and amplitude functions of two dimensional Turing patterns consisting of rhombic arrays of rectangles and hexagonal is obtain by singular perturbations theory. Finally, by the method of computer simulation of the model, we describe two different patterns.