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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 $\dot x=xF(r(c(t)),x)$. The authors provide several sufficient conditions on F, r and c such that the solution x satisfies $$ \limsup\sb{t\to +\infty}x(t)>0,\quad or\quad \liminf\sb{t\to +\infty}x(t)>0\quad or\quad \liminf\sb{t\to +\infty}t\sp{-1}\int\sp{t}\sb{0}x(s)ds>0. $$ 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

92D25Population dynamics (general)
34D05Asymptotic stability of ODE
Full Text: DOI
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