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Article Dans Une Revue Journal of Theoretical Biology Année : 2011

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

Résumé

This article re-analyses a prey-predator model with a refuge introduced by one of the founders of population ecology G.F. Gause and his co-workers to explain discrepancies between their observations and predictions of the Lotka-Volterra prey-predator model. They replaced the linear functional response used by Lotka and Volterra by a saturating functional response with a discontinuity at a critical prey density. At concentrations below this critical density prey were effectively in a refuge while at a higher densities they were available to predators. Thus, their functional response was of the Holling type III. They analyzed this model and predicted existence of a limit cycle in predator-prey dynamics. In this article I show that their model is ill posed, because trajectories are not well defined. Using the Filippov method, I define and analyze solutions of the Gause model. I show that depending on parameter values, there are three possibilities: (1) trajectories converge to a limit cycle, as predicted by F.G. Gause, (2) trajectories converge to an equilibrium, or (3) the prey population escapes predator control and grows to infinity.
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Dates et versions

hal-00671831 , version 1 (19-02-2012)

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Vlastimil Křivan. On the gause predator-prey model with a refuge: a fresh look at the history. Journal of Theoretical Biology, 2011, 274 (1), pp.67. ⟨10.1016/j.jtbi.2011.01.016⟩. ⟨hal-00671831⟩

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