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Local and global stability for population models

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Abstract

In general, local stability does not imply global stability. We show that this is true even if one only considers population models.

We show that a population model is globally stable if and only if it has no cycle of period 2. We also derive easy to test sufficient conditions for global stability. We demonstrate that these sufficient conditions are useful by showing that for a number of population models from the literature, local and global stability coincide.

We suggest that the models from the literature are in some sense “simple”, and that this simplicity causes local and global stability to coincide.

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Authors and Affiliations

  1. Department of Computer Science, Oregon State University, 97331, Corvallis, OR, USA

    P. Cull

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  1. P. Cull
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Cull, P. Local and global stability for population models. Biol. Cybern. 54, 141–149 (1986). https://doi.org/10.1007/BF00356852

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  • DOI: https://doi.org/10.1007/BF00356852

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