Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 60, pp. 1-11.

Title: Permanence in logistic and Lotka-Volterra
       systems with dispersal and time delays
       
Authors: Jingan Cui (Nanjing Normal Univ., China)
         Mingna Guo (Nanjing Normal Univ., China)

Abstract: 
 In this paper, we consider the effect of dispersal on the
 permanence of single and interacting populations modelled by
 systems of integro differential equations. Different from
 former studies, our discussion here includes the important
 situation when species live in a weak  patchy environment;
 i.e., species in some isolated patches will  become extinct
 without the contribution from other patches.
 For the single population model considered in this paper,
 we show that the same species can persist for some
 dispersal rates and the species will vanish in some isolated
 patches. Based on the results for a single population model, we
 derive sufficient conditions for the permanence of two interacting
 competitive and predator-prey dispersing systems.  
 
Submitted November 24, 2004. Published June 10, 2005.
Math Subject Classifications: 92D25, 34C60, 34K20.
Key Words: Logistic equation; Lotka-Volterra system; dispersal;
           permanence; extinction; time delay.