Instability induced by cross-diffusion in reaction–diffusion systems

In this paper the instability of the uniform equilibrium of a general strongly coupled reaction–diffusion is discussed. In unbounded domain and bounded domain the sufficient conditions for the instability are obtained respectively. The conclusion is applied to the ecosystem, it is shown that cross-diffusion can induce the instability of an equilibrium which is stable for the kinetic system and for the self-diffusion–reaction system.