Global Stability of a System of Two Interacting Species with Convective and Dispersive Migration

Using Liapunov's direct method, effects of convective and dispersive migration on the global stability of the equilibrium state of a system of two interacting species are investigated. It is shown that the stable equilibrium state without dispersal remains so with dispersal. Further, it is pointed out that stability or instability of the equilibrium state of the system is not affected by convective migration. These results are justified in cases of a system of mutualistic interactions of species and a prey-predator system with functional response.