Permanence and asymptotic stability for competitive and Lotka-Volterra systems with diffusion

Abstract

Using an iterative monotone scheme and comparison theorems for differential equations we prove for the reaction-di)usion system, ut = D1(t)Δu + u(a(t) - b(t)u - c(t)v), vt = D2(t)Δu + v(-d(t) + e(t)u - f(t)v), (t;x) ε [0,∞) x Ω, with Twith T-periodic coefficients, the existence of a spatially homogeneous positive periodic solution which is a global attractor. We also give results on permanence and extinction. © 2003 Published by Elsevier Science Ltd.