The effects of the functional response on the bifurcation behavior of a mite predator–prey interaction model
The effects of the functional response on the bifurcation behavior of a mite predator–prey interaction model
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DOI：
10.1007/s002850050095
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发表时间：
1997-11
影响因子：
1.9
通讯作者：
J. B. Collings
中科院分区：
文献类型：
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作者：
J. B. Collings
一个捕食者-猎物相互作用模型的基础上的微分方程系统的温度依赖的参数选择适当的螨相互作用的苹果树进行了分析，以确定如何的功能性反应的类型影响分歧和稳定性行为。被认为是第一，第二，第三，和第四类功能性反应，其中最后一个包括猎物干扰捕食。结果表明，具有I，II和III型功能响应的模型系统在温度参数的定义范围内表现出定性相似的分岔和稳定行为。类似的行为被发现在系统中的IV型功能性反应在低水平的猎物干扰。更高水平的干扰是不稳定的，如双稳态的流行和存在的三个吸引子的模型参数的一些值所示。所有四个系统都能够模拟种群波动和爆发。
A predator–prey interaction model based on a system of differential equations with temperature-dependent parameters chosen appropriately for a mite interaction on apple trees is analyzed to determine how the type of functional response influences bifurcation and stability behavior. Instances of type I, II, III, and IV functional responses are considered, the last of which incorporates prey interference with predation. It is shown that the model systems with the type I, II, and III functional responses exhibit qualitatively similar bifurcation and stability behavior over the interval of definition of the temperature parameter. Similar behavior is found in the system with the type IV functional response at low levels of prey interference. Higher levels of interference are destabilizing, as illustrated by the prevalence of bistability and by the presence of three attractors for some values of the model parameters. All four systems are capable of modeling population oscillations and outbreaks.