一类H-V功能性反应的捕食系统的持续性与稳定性分析

Permanence and Stability of Predator-prey System with Hassell-Varley Type Functional Response

分析了Hassell-Varley功能性反应的捕食系统的动力学行为。首先建立了一个新的具有H-V型功能性反应捕食系统的数学模型。然后给出持续生存的定义和两个基本引理,通过运用比较原理和分析技巧,获得了该捕食者-食饵系统的持续生存的充分条件。利用线性化方法和矩阵性质,得到系统在正平衡点局部渐近稳定。最后利用线性化方法,获得具常系数H-V功能性反应的捕食系统的局部稳定的充分条件。所得结果是新的,扩展了相关文献的一些结论。

This paper discusses the permanence and stability of predator-prey system with Hassell-Varley type functional response.Firstly,a new model of the system is formulated.Then,by the skills of inequalities,we obtain a sufficient condition ensuring the permanence for predator-prey system is obtained.Finally,based on the results,stability of system is derived by using matrix theory.The obtained results are novel and improve some ones in existing publications.