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Asymptotic properties of the positive equilibrium of a discrete survival model. (English) Zbl 1064.39009

It is shown that every positive solution of \(x_{n+1}= (1-\mu)x_n+ p\exp(-\nu x_{n-k})\) with \(0<\mu< 1\), positive \(\nu\), \(p\) and \(k\in\mathbb{N}_0\) is persistent. Conditions are given such that every solution \(x_n\) oscillates about the equilibrium \(x^*\), that \(x^*\) is locally asymptotically stable, and that \(x_n\to x^*\) as \(n\to\infty\), respectively.

MSC:

39A11 Stability of difference equations (MSC2000)
92D25 Population dynamics (general)
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