具Monod-Haldane功能反应的四种群食饵-捕食脉冲系统的动力学分析

Dynamic Analysis of a Four-Species Prey-predator Impulsive System with a Monod-Haldane Functional

基于害虫综合管理策略,本文利用脉冲比较定理、Floquent理论及微小扰动法,研究了一类具有Monod-Haldane功能反应、脉冲比例收获和脉冲常数投放的四种群食饵–捕食系统的动力学性质,证明了系统两食饵灭绝和持续生存的充分条件,而且给出了一食饵种群灭绝其余三种群持续生存的两个充分条件。数值模拟表明,随着投放量的增加,系统出现拟周期分支、倍周期分支、混沌、半周期分支等复杂的动力学性质。

Basing on the strategy of integrated biology management and using the impulsive com-parison theorem,the Floquent theory and the small amplitude perturbation skill,we investigate the dynamical properties of a four-species prey-predator impulsive system with a Monod-Haldane func-tional response,impulsive ratio harvest and impulsive release.Suffcient conditions for the system of the two preys to be extinct and permanence are proved.Moreover,the two suffcient conditions of which the extinction for one of the four preys and the permanence of remaining species are given.Numerical simulation shows that,with the increasing of immigration,the system has more complex dynamics including the quasi-periodic bifurcation,periodic doubling bifurcation,chaos,periodic halv-ing bifurcation,etc.