Reflections and Calculations on a Prey-Predator-Patch Problem [chapter]

O. Diekmann, J. A. J. Metz, M. W. Sabelis
1989 Evolution and Control in Biological Systems  
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
more » ... implified system is analysed and the existence of multiple stable steady states is demonstrated. 1980 Mathematics Subject Classification: 92A15
doi:10.1007/978-94-009-2358-4_4 fatcat:6dv2xf2v4veefil7us5zmfnpi4