Reflections and calculations on a prey-predator-patch problem

✍ Scribed by O. Diekmann; J. A. J. Metz; M. W. Sabelis

• Publisher: Springer Netherlands
• Year: 1989
• Tongue: English
• Weight: 561 KB
• Volume: 14
• Category: Article
• ISSN: 0167-8019
• DOI: 10.1007/bf00046671

✦ Synopsis

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.