Persistence in nonautonomous predator–prey systems with infinite delays

Persistence in nonautonomous predator–prey systems with infinite delays

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Article ID: iaor20071205
Country: Netherlands
Volume: 197
Issue: 2
Start Page Number: 302
End Page Number: 321
Publication Date: Dec 2006
Journal: Journal of Computational and Applied Mathematics
Authors: ,
Keywords: Volterra equations
Abstract:

This paper studies the general nonautonomous predator–prey Lotka–Volterra systems with infinite delays. The sufficient and necessary conditions of integrable form on the permanence and persistence of species are established. A very interesting and important property of two-species predator–prey systems is discovered, that is, the permanence of species and the existence of a persistent solution are each other equivalent. Particularly, for the periodic system with delays, applying these results, the sufficient and necessary conditions on the permanence and the existence of positive periodic solutions are obtained. Some well-known results on the nondelayed periodic predator–prey Lotka–Volterra systems are strongly improved and extended to the delayed case.

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