Permanence and extinction in nonlinear single and multiple species system with diffusion

In this paper, we consider the effect of diffusion on the permanence and extinction of single and multiple endangered species that live in changing patch environments. Average conditions are obtained for the permanence and extinction of the systems considered. The results obtained in this paper generalize the main results of Cui and Chen [The effect of diffusion on the time varying logistic population growth, Comput. Math. Appl. 36(3) (1998) 1-9, Permanence and extinction in logistic and Lotka-Volterra systems with diffusion, J. Math. Anal. Appl. 258(2) (2001) 512-535].