PERMANENCE IN KOLMOGOROV COMPETITION MODELS WITH DIFFUSION

In this paper, the authors consider the 'permanence' problem for two-s pecies periodic Kolmogorov competition reaction-diffusion systems defi ned on a bounded domain subject to Neumann boundary conditions. The ma in result, based on comparison and maximum principle arguments, provid es sufficient conditions for permanence and is illustrated in applicat ion to the Lotka-Volterra competition system as well as to a general c lass of reaction-diffusion systems. The significance of permanence in biological systems in general is discussed.