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Local and Global Stability of Discrete One-Dimensional Population Models

In: Biomathematics and Related Computational Problems

Author

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  • Paul Cull

    (Oregon State University, Department of Computer Science)

Abstract

Local and global stability do not necessarily coincide even for one-humped discrete models. We give several sufficient conditions for global stability, and use these conditions to show that for the usual population models from the litterature, local and global stability do coincide. The sufficient conditions also imply that local and global stability coincide for slightly more complicated models. We give examples of the simplest models which are locally but not globally stable. We give a new method for testing for local stability when the derivative is -1 at the equilibrium point. The usual models from the litterature are locally and globally stable when this derivative is -1.

Suggested Citation

  • Paul Cull, 1988. "Local and Global Stability of Discrete One-Dimensional Population Models," Springer Books, in: Luigi M. Ricciardi (ed.), Biomathematics and Related Computational Problems, pages 271-278, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-2975-3_24
    DOI: 10.1007/978-94-009-2975-3_24
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