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Reflections and Calculations on a Prey-Predator-Patch Problem

In: Evolution and Control in Biological Systems

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  • O. Diekmann

    (Centre for Mathematics and Computer Science
    University of Leiden, Institute of Theoretical Biology)

  • J. A. J. Metz

    (University of Leiden, Institute of Theoretical Biology)

  • M. W. Sabelis

    (University of Leiden, Department of Population Biology)

Abstract

This paper is concerned with models for the interaction of plants, herbivores and their predators. We concentrate on situations in which local colonies of herbivores either over-exploit their host plant or are driven to extinction by predators. Starting from a complicated structured model, in which the local prey and predator density within patches is taken into account, we use time scale arguments to derive a three dimensional system of ordinary differential equations. The simplified system is analysed and the existence of multiple stable steady states is demonstrated.

Suggested Citation

  • O. Diekmann & J. A. J. Metz & M. W. Sabelis, 1989. "Reflections and Calculations on a Prey-Predator-Patch Problem," Springer Books, in: A. B. Kurzhanski & K. Sigmund (ed.), Evolution and Control in Biological Systems, pages 23-35, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-2358-4_4
    DOI: 10.1007/978-94-009-2358-4_4
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