一类具Holling Ⅳ功能反应的两食饵一捕食者脉冲系统的动力学性质  

Dynamic Behavior of Two-prey One-predator Impulsive System with Holling Ⅳ Functional Response

作　　者：黄文韬[1] 吴兴杰[2] 李伟[2] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004 [2]合肥师范学院数学系,安徽合肥230061

出　　处：《南京理工大学学报》2009年第5期619-625,共7页Journal of Nanjing University of Science and Technology

基　　金：国家自然科学基金(10871206);广西高校优秀人才资助计划

摘　　要：基于害虫综合管理策略,研究了具有Holling Ⅳ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动力学性质,利用脉冲比较定理、Floquent理论及微小扰动法,给出了投放临界值,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两种群持续生存的2个充分条件。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、半周期分支等复杂的动力学性质。Based on the strategy of integrated pest management, the dynamic behavior of a two-prey one-predator system with Holling IV functional response, impulsive ratio harvest and constant impulsive release is investigated. By using impulsive comparison theorem, Floquent theory and small amplitude perturbation skill, the critical value of impulsive release is given. One sufficient condition for the two preys to be extinct is proved, and the permanence of the system is proved. Moreover, the two sufficient conditions for the extinction of one of two preys and the permanence of remaining species are given. Numerical simulation shows that： with the increase of constant release, the system has more complex dynamics including periodic doubling bifurcation, chaos and periodic halving bifurcation.

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

分 类 号：O175.12[理学—数学]