Dynamic behavior of a nonlinear single species diffusive system

In this paper, we consider the following nonlinear single species diffusive system (x) over dot(i)(t) = x(i)(t) (b(i)(t) - Sigma(li)(k=1) a(i)k(t)(x(i)(t))beta(ik)) +Sigma D-n(j=1)ij(t)(x(j)(t)-x(i)(t)), (i,j=1,2,...,n), where b(i)(t),a(ik)(t),D-ij(t),i,j = 1,2,...,n;k = 1,2,...,l(i) are all continuous omega-periodic functions, and beta(ik), i = 1, 2,...,n;k = 1, 2,...,l(i) are positive constants. Sufficient conditions which guarantee the permanence, extinction and existence of a unique globally attractive positive omega-periodic solution are obtained. Examples together with their numeric simulations show the feasibility of the main results.