Abstract
In this paper, a general class of nonautonomous Lotka-Volterra dispersal system with discrete and continuous infinite delays is investigated. This class of Lotka-Volterra systems model the diffusion of a single species into n patches by discrete dispersal. By using Schauder's fixed point theorem, we prove the existence of positive periodic solutions of system. The global asymptotical stability of positive periodic solution is discussed and the sufficient conditions for exponential stability are also given. we give an example to illustrate the validity of the results in the end. The conditions we obtained are more general and it can be extended to several special systems.
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