Chemical formation of spatial patterns induced by nonlinearity in a concentration-dependent diffusion coefficient

Studies of pattern growth through coupling of reaction/diffusion have concentrated so far on strong nonlinearities in reaction kinetics. We report that pattern growth can be induced by nonlinearity in a concentration-dependent diffusion term, coupled to weakly nonlinear simple reaction schemes (2A → C). According to the model the diffusion coefficient is constant at low concentration. However, there is a smooth transition to reciprocal dependency on the concentration at higher values; i.e., the diffusion becomes slower as concentration increases. Fast Fourier transform algorithms are used for two-dimensional numerical solutions of the kinetics equations.