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Persistence in population models with demographic fluctuations. (English) Zbl 0606.92022

In this paper the asymptotic behavior of a population is discussed which is governed by an equation of the form x ˙=xF(r(c(t)),x). The authors provide several sufficient conditions on F, r and c such that the solution x satisfies

lim sup t+ x(t)>0,orlim inf t+ x(t)>0orlim inf t+ t -1 0 t x(s)ds>0·

It could, however, be mentionable that the original idea in investigating such equations with nonautomonous factors is due to Volterra by considering these as seasonal factors.

Reviewer: G.Karakostas

MSC:
92D25Population dynamics (general)
34D05Asymptotic stability of ODE
92D40Ecology
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