鼠类-天敌系统渐近稳定性的数学分析

Mathematical Analysis on Asymptotic Stability of Rodent-Predator System

天敌能否控制鼠害是鼠害防治实践中最重要的课题之一,通过建立鼠类-天敌系统的捕食-食饵离散模型,推导出自然生态条件下鼠类数量与天敌数量的平衡关系以及鼠类-天敌系统渐近稳定的判定条件,数学分析表明,天敌对鼠的数值反应、功能反应以及鼠类种群繁殖调节是系统能够渐近稳定的决定因素。

It is one of the important problems in the 1PM whether predators can control rodent damage. A discrete model is proposed which consists of the rodent and predator, in order to deduce the quantity equilibrium formula between rodent and predator in natural ecosystem and the decisive condition of asymptotic stability. This analysis shows that the numerical response and functional response of predator and the self-regulation in the rodents' population are to maintain the systimatical equilibrium.