Diffusion induced homogeneity breaking instability of the solutions in a reaction-diffusion Sporns-Seelig system

One of the key concerns in the computational biology is to declare the underlying mechanisms involved in the spatiotemporal pattern formations. In this paper, we mainly focus on the existence, stability/instability and the diffusion induced homogeneity breaking instability of both the positive constant equilibrium solution and the Hopf bifurcating spatially homogeneous periodic solutions. The onset of the instabilities of above two kinds of solutions will bring out the emergence of the spatiotemporal patterns. Our findings facilitate a more clearer comprehension of the mechanisms underlying the pattern formations in this specific chemical reaction model.