非自治脉冲HollingⅡ捕食系统的研究

Study of a Nonautonomous HollingⅡ Predator-Prey System with Impulses

研究了HollingⅡ捕食系统在受其他因素干扰、系数变化和脉冲扰动时的动力学行为.首先对单种群脉冲非自治系统的动力学行为进行了讨论,分析了单种群系统持续生存和灭绝的条件.进一步,应用这些结论和微分方程比较定理,分别对系统食饵灭绝和食饵捕食者都灭绝的情况进行了研究,并讨论了系统的持久生存性,得到了带脉冲的HollingⅡ非自治捕食系统灭绝和持久生存的条件.

The dynamical behaviors of Holling II predator-prey system which were disturbed by some effects,coefficients varied and impulses perturbed were studied.Firstly,the dynamical behaviors of single-species impulses nonautonomous system were discussed,and the permanence and extinction conditions of single-species system were analyzed.Further,based on these results and impulsive differential comparison theorem,the system prey extinction and both prey and predator extinction were studied respectively,and the permanence of system was discussed,the extinction and permanence conditions of Holling II nonautonomous predator-prey system with impulses were obtained.