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The dynamics of some discrete population models. (English) Zbl 0760.92019

The authors consider the discrete delay equation \[ x_{n+1}=\lambda x_ n+F(x_{n-m}),\tag{E} \] where \(F\) is a nonnegative, real-valued function defined on \(\mathbb{R}^ +\), \(\lambda\in\mathbb{R}\) with \(0<\lambda<1\) and \(m\) a positive integer. Sufficient conditions are provided that all positive solutions of (E) converge as \(n\to\infty\) for the case that \(F\) is of the form \(F=f\cdot g\) and \(F=f+g\), where \(f\) is a positive and decreasing function and \(g\) a non-negative increasing function.
The obtained results are applied to the discrete version of models that have been proposed for a homogeneous population of mature circulating white blood cells, of the model of the dynamics of the so-called Nicholson’s blowflies and of a model describing the dynamics of the red blood cells system.
Reviewer: D.Dorninger (Wien)

MSC:

92D25 Population dynamics (general)
39A12 Discrete version of topics in analysis
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References:

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