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Periodic solution and almost periodic solution for a nonautonomous Lotka-Volterra dispersal system with infinite delay. (English) Zbl 1141.34043
The authors deal with a nonautonomous Lotka-Volterra system with infinite delay modeling the diffusion of a single species into $$n$$ patches by discrete dispersal. Some sufficient conditions are established for the uniform persistence and the global asymptotic stability of the general nonautonomous system. Moreover, when the system is of periodic type or almost periodic type, the existence and the globally asymptotic stability of a positive periodic or almost periodic solution are proved, respectively. The approaches are standard involving a continuation theorem of coincidence degree and Lyapunov’s second method.

##### MSC:
 34K13 Periodic solutions to functional-differential equations 92D25 Population dynamics (general) 34K25 Asymptotic theory of functional-differential equations
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