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Persistence in nonautonomous predator–prey systems with infinite delays. (English) Zbl 1110.34054
This paper is concerned with a persistence of the general nonautonomous predator-prey Lotka- Volterra systems, in which both finite and infinite delays appear in the interaction terms. Sufficient and necessary conditions of integrable form for permanence and persistence of species are established. It is proved that the permanence of species and the existence of a persistent solution are equivalent to each other. Moreover, some sufficient and necessary conditions for permanence and the existence of positive periodic solutions are also established. The result in this paper even improves and extents some conclusions with no delay.
MSC:
34K25Asymptotic theory of functional-differential equations
92D25Population dynamics (general)
34K13Periodic solutions of functional differential equations