Parametric analysis of the ratio-dependent predator-prey model
Parametric analysis of the ratio-dependent predator-prey model
复制标题
DOI：
10.1007/s002850000078
复制
发表时间：
2001-09-01
影响因子：
1.9
通讯作者：
Arditi, R
中科院分区：
文献类型：
--
作者：
Berezovskaya, F;Karev, G;Arditi, R
本文对一类功能性反应是食饵和捕食者丰度比的函数的常微分方程模型的稳定性和动力学性质进行了完整的参数分析，证明了在不同的参数值下，系统存在八种不同性质的行为.特别是，存在共存区域（可能是稳定的或振荡的），两个种群灭绝的区域，以及取决于初始值的“条件共存”区域。比率依赖模型区别于其他捕食模型的一个主要数学特征是原点是一个复杂的平衡点，原点的性质决定了模型的主要性质。这是第一次在生态模型中展示这种现象。利用常微分方程定性理论和分支理论对模型进行了研究。生物相关性的数学结果进行了讨论保护问题（共存是理想的）和生物控制（灭绝是理想的）。
We present a complete parametric analysis of stability properties and dynamic regimes of an ODE model in which the functional response is a function of the ratio of prey and predator abundances, We show the existence of eight qualitatively different types of system behaviors realized for various parameter values. In particular, there exist areas of coexistence (which may be steady or oscillating), areas in which both populations become extinct, and areas of "conditional coexistence" depending on the initial values. One of the main mathematical features of ratio-dependent models, distinguishing this class from other predator-prey models, is that the Origin is a complicated equilibrium point, whose characteristics crucially determine the main properties of the model. This is the first demonstration of this phenomenon in an ecological model. The model is investigated with methods of the qualitative theory of ODEs and the theory of bifurcations. The biological relevance of the mathematical results is discussed both regarding conservation issues (for which coexistence is desired) and biological control (for which extinction is desired).