捕食者具阶段结构和脉冲扰动的群体防卫捕食系统  

Group defense predator-prey system with stage-structured and impulsive perturbations on predator

作　　者：李顺异[1] 唐兴芸[1] 薛先贵[1] 

机构地区：[1]黔南民族师范学院数学系,贵州都匀558000

出　　处：《纯粹数学与应用数学》2012年第6期765-773,共9页Pure and Applied Mathematics

基　　金：贵州省教育厅青年项目基金([2010]096);贵州省重点支持学科(应用数学)基金([2009]303)

摘　　要：研究了一类捕食者具有阶段结构与脉冲扰动和食饵具有群体防卫效应的捕食系统,应用Floquet乘子理论和脉冲比较定理,获得了食饵(害虫)灭绝周期解局部稳定和系统持续生存的充分条件.通过数值例子讨论了脉冲周期,成年捕食者(天敌)的投放量和群体防卫效应系数对系统的重要作用,并揭示了系统诸如周期与拟周期振荡,混沌,吸引子突变等复杂的动力学现象.为实际的害虫管理提供了可靠的策略依据.A prey-predator system with group defense for prey, stage-structured and impulsive perturbation for predator is considered. By using Floquet theorem and comparison theorem of impulsive differential equation, the sufficient conditions for locally stable of prey-eradication periodic solution and permanence of the system are obtained. The importance of the impulsive period, the released amount of mature predator and the coefficient of group defense effect are discussed by numerical examples, and show that the system considered has more complicated dynamics, such as periodic and quasi-periodic oscillation, chaos, attractor crisis, etc. Our results provide reliable strategy basis for practical pest management.

关 键 词：阶段结构 群体防卫 脉冲扰动 持续生存 混沌 

分 类 号：O175[理学—数学]