کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6371421 | 1318922 | 2011 | 7 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On the Gause predator-prey model with a refuge: A fresh look at the history
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کلمات کلیدی
موضوعات مرتبط
علوم زیستی و بیوفناوری
علوم کشاورزی و بیولوژیک
علوم کشاورزی و بیولوژیک (عمومی)
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چکیده انگلیسی
This article re-analyses a prey-predator model with a refuge introduced by one of the founders of population ecology 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 Gause, (2) trajectories converge to an equilibrium, or (3) the prey population escapes predator control and grows to infinity.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Theoretical Biology - Volume 274, Issue 1, 7 April 2011, Pages 67-73
Journal: Journal of Theoretical Biology - Volume 274, Issue 1, 7 April 2011, Pages 67-73
نویسندگان
Vlastimil KÅivan,