Cross-diffusion driven instability in a two toxin producing competitive species of reaction diffusion system

Abstract

We have proposed a diffusion model of a two toxin producing com- petitive species. In absence of diffusion the system is stabilized by the effect of toxin substances. It can also be shown that self diffusion can not influence on the stability of the system but cross-diffusion has an important role to pattern formation. Stability-instability of reaction- diffusion system has been analyzed with respect to L2 norm. It is observed that cross-diffusion can destabilize the system stabilized by toxin substances.