Lyapunov functions for Lotka-Volterra predator-prey models with optimal foraging behavior
Lyapunov functions for Lotka-Volterra predator-prey models with optimal foraging behavior
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DOI：
10.1007/s002850050009
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发表时间：
1999-12-01
影响因子：
1.9
通讯作者：
Krivan, V
中科院分区：
文献类型：
--
作者：
Boukal, DS;Krivan, V
最优觅食理论预测消费者行为的突然变化会导致功能反应的不连续性。因此，具有最优觅食行为的种群动力学模型可以用右端不连续的微分方程来描述。本文研究了三个具有最优觅食行为的Lotka-Volterra捕食系统的行为。我们研究了具有替代食物的捕食者-食饵模型，具有移动的捕食者和常驻食饵的两斑块模型，以及捕食者和食饵都具有移动的的两斑块模型。我们表明，在研究的例子中，最佳觅食行为改变中立稳定固有的Lotka-Volterra系统的存在一个有界的全局吸引子。分析是基于建设和使用适当的李雅普诺夫函数的模型描述的不连续微分方程。
The theory of optimal foraging predicts abrupt changes in consumer behavior which lead to discontinuities in the functional response. Therefore population dynamical models with optimal foraging behavior can be appropriately described by differential equations with discontinuous right-hand sides. In this paper we analyze the behavior of three different Lotka-Volterra predator-prey systems with optimal foraging behavior. We examine a predator-prey model with alternative food, a two-patch model with mobile predators and resident prey, and a two-patch model with both predators and prey mobile. We show that in the studied examples, optimal foraging behavior changes the neutral stability intrinsic to Lotka-Volterra systems to the existence of a bounded global attractor. The analysis is based on the construction and use of appropriate Lyapunov functions for models described by discontinuous differential equations.