一类具有Beddington-DeAngelis功能反应和脉冲效应的两食饵一捕食者系统的动力学性质  

Dynamic Properties of Tow-Prey One-Predator System with Beddington-DeAngelis Functional Response and Impulsive Effect

作　　者：黄燕革[1] 吴兴杰[2] 秦桂毅[3] 黄勇[1] 

机构地区：[1]百色学院数学与计算机信息工程系,广西百色533000 [2]合肥师范学院数学系,安徽合肥230061 [3]桂林师范高等专科学校数学与计算机科学系,广西桂林541001

出　　处：《四川师范大学学报（自然科学版）》2011年第3期325-330,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(10961011);安徽省高等学校省级自然科学基金(KJ2010B164)资助项目

摘　　要：基于害虫综合管理策略,利用脉冲比较定理、Floquent理论及微小扰动法,研究了具有Beddington-DeAngelis功能反应、脉冲比例收获和脉冲常数投放的两食饵一捕食者系统的复杂动力学性质,给出了投放临界值,得到了系统灭绝、持续生存及一食饵种群灭绝其余两种群持续生存的充分条件.数值模拟表明,随着投放量的增加,系统出现倍周期分支、混沌、吸引子危机、半周期分支等复杂的动力学行为.In this paper,based on the strategy of integrated biology management,a class of tow-prey one-predator system with Beddington-DeAngelis functional response,impulsive ratio harvest and impulsive release is established.By using impulsive comparison theorem,Floquent theory and small amplitude perturbation skill,the critical value of impulsive immigration and sufficient conditions for the system to be extinct and permanence are proved.Moreover,the two sufficient conditions for the extinction of one of two prey and permanence of predator are given.Numerical simulation shows that with the increasing of immigration the system has more complex dynamics including periodic doubling bifurcation,chaos,crises,periodic halving bifurcation,etc.

关 键 词：两食饵一捕食者系统 脉冲微分方程 脉冲比较定理 混沌 Floquent理论 

分 类 号：O175.12[理学—数学]