一类非二次微分食饵—捕食系统的脉冲控制

Impulsive Control of a Series of Non 2th-Differential Predator-Prey System

利用脉冲微分方程的比较原理对一个具有功能反应函数为x^(1/2)的食饵—捕食生物模型进行研究.考虑到模型存在的不确定性,研究了捕食者的捕食率不但受食饵的密度大小影响,同时还受捕食者本身的密度影响的生物系统.通过脉冲控制得到了使其渐近稳定到原先不稳定的正平衡点的充分条件,使食饵密度和捕食者密度保持在一个定数附近并给出了生态解释.

This paper investigates a predator-prey ecosystem with functional reaction function √x by using comparison theorem of impulsive differential system. Considering the uncertainty of this system, the paper thinks over that the efficiency of predator is affected by not only prey＇s density but also predator＇s density. Then we get the sufficient condition for this system＇s unstable positive equilibrium to asymptotic stability by the impulsive control. And densities of predator and prey individually exist around a constant. Finally, it gives ecological explanation.