Global stability in diffusive delay Lotka-Volterra systems

We consider the global asymptotic stability of diffusive delay Latka-Volterra systems which may model population dynamics of closed ecological environments containing n interacting species. The first part of this paper deals with discrete delay case, where both continuous and discrete diffusion situations are considered. The second part of this paper studies unbounded continuous delay cases, where the integral kernels are assumed to satisfy linear differential equations with constant coefficients. In both parts, sufficient conditions for global asymptotic stability of the unique positive steady states are derived via some proper Lyapunov functions. To some extent, these results indicate that the diffusivity of the system may not affect the global asymptotic stability of its reaction system.