Qualitative analysis of a predator-prey system with limit cycles

✍ Scribed by Torsten Lindström

• Publisher: Springer
• Year: 1993
• Tongue: English
• Weight: 989 KB
• Volume: 31
• Category: Article
• ISSN: 0303-6812
• DOI: 10.1007/bf00161198

✦ Synopsis

Fairly regular multiannual microtine rodent cycles are observed in boreal Fennoscandia. In the southern parts of Fennoscandia these multiannual cycles are not observed. It has been proposed that these cycles may be stabilized by generalist predation in the south.

We show that if the half-saturation of the generalist predators is high compared to the number of small rodents the cycles are likely to be stabilized by generalist predation as observed. We give examples showing that if the half-saturation of the generalist predators is low compared to the number of small rodents, then multiple equilibria and multiple limit cycles may occur as the generalist predator density increases.