On the Gause predator-prey model with a refuge: A fresh look at the history

0355868 - BC 2012 RIV GB eng J - Journal Article
Křivan, Vlastimil
On the Gause predator-prey model with a refuge: A fresh look at the history.
Journal of Theoretical Biology. Roč. 274, č. 1 (2011), s. 67-73. ISSN 0022-5193. E-ISSN 1095-8541
Grant - others:Department of Agriculture(US) EF-0832858
Institutional research plan: CEZ:AV0Z50070508
Keywords : discontinuous differential equations * Filippov solution * holling functional response
Subject RIV: EH - Ecology, Behaviour
Impact factor: 2.208, year: 2011

This article re-analyses the Gause prey–predator model with a refuge. The model is described by a differential equation with a discontinuity in the right hand-side , and trajectories are defined in the Filippov sense.The article shows that depending on parameter values, there are threepossibilities: (1) trajectories converge to a limit cycle, aspredicted by Gause, (2) trajectories converge to an equilibrium, or (3) the prey population escapes predator control and grows to infinity.
Permanent Link: http://hdl.handle.net/11104/0194538