A global attractivity result for a discrete time system, with applications to density dependent population dynamics models. (Q2763767)
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scientific article; zbMATH DE number 1693107
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A global attractivity result for a discrete time system, with applications to density dependent population dynamics models. |
scientific article; zbMATH DE number 1693107 |
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3 September 2002
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population dynamics
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global attractor
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discrete time dynamical system
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matrix models
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A global attractivity result for a discrete time system, with applications to density dependent population dynamics models. (English)
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The author proves a result on global stability in the state space, local in the parameter space, of a fixed point of a time discrete matrix model, conditionally to the uniqueness of this nonzero fixed point.NEWLINENEWLINE The proofs are based on the theory of dissipative dynamical systems and on a reduction result related to the existence of invariant manifolds of discrete dynamical systems in Banach spaces.NEWLINENEWLINE Two applications to discrete time density dependent population dynamics problems are given. The first of them is a scalar delay difference equation and the second one a discrete time and age structured model. In both cases the author proves convergence of the solutions to a unique nontrivial equilibrium solution.
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