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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 $\stackrel{˙}{x}=xF\left(r\left(c\left(t\right)\right),x\right)$. The authors provide several sufficient conditions on F, r and c such that the solution x satisfies

$\underset{t\to +\infty }{lim sup}x\left(t\right)>0,\phantom{\rule{1.em}{0ex}}or\phantom{\rule{1.em}{0ex}}\underset{t\to +\infty }{lim inf}x\left(t\right)>0\phantom{\rule{1.em}{0ex}}or\phantom{\rule{1.em}{0ex}}\underset{t\to +\infty }{lim inf}{t}^{-1}{\int }_{0}^{t}x\left(s\right)ds>0·$

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:
 92D25 Population dynamics (general) 34D05 Asymptotic stability of ODE 92D40 Ecology
##### References:
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