| 引用本文： |
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李祖雄,黄健民,陈飞.具有脉冲效应的Holling Ⅲ系统的动力行为[J].广西科学,2006,13(4):255-260. [点击复制]
- LI Zu-xiong,HUANG Jian-min,CHEN Fei.Analysis of a Holling Type Ⅲ Predator System with Impulsive Effect[J].Guangxi Sciences,2006,13(4):255-260. [点击复制]
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| 摘要: |
通过周期性释放天敌和化学控制的综合害虫管理(IPM)改进捕食者具有Holling型功能性反应系统:{(dy(t)/dt)=-cy(t)+(kαx2(t)y(t)/x2(t)+β2).(dx(t)/dt)=ax(t)-bx2(t)-(αx2(t)y(t)/x2(t)+β2),
得到一个新的系统:{(dy(t)/dt)=-cy(t)+(kαx2(t)y(t)/x2(t)+β2).(dx(t)/dt)=ax(t)-bx2(t)-(αx2(t)y(t)/x2(t)+β2),}t≠nT,{Δy(t)=-p2y(t)+q.Δx(t)=-p1x(t),}t=nT.给出当q>0,0≤p1<1,0≤p2<1时,新系统的害虫周期全局渐近稳定性与新系统的持续生存条件.研究当q>0,0≤p1<1,0≤p2<1时,新系统正周期解的存在性和当q≡0,0<p1<1,0≤p2<1时,无捕食者周期解的存在性和稳定性. |
| 关键词: HollingⅢ类功能反应 脉冲效应 全局渐近稳定性 持续生存 分支 |
| DOI： |
| 投稿时间：2006-04-14修订日期：2006-06-23 |
| 基金项目:国家自然科学基金(10461002)资助 |
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| Analysis of a Holling Type Ⅲ Predator System with Impulsive Effect |
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LI Zu-xiong, HUANG Jian-min, CHEN Fei
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| (Mathematics Science College, Guangxi Normal University, Guilin, Guangxi, 541004, China) |
| Abstract: |
By introducing a constant periodic releasing natural enemies and integrated pest management,we devolop the system where the predator has Holling type Ⅲ functional response:{(dy(t)/dt)=-cy(t)+(kαx2(t)y(t)/x2(t)+β2).(dx(t)/dt)=ax(t)-bx2(t)-(αx2(t)y(t)/x2(t)+β2),
At the sametime,we obtain a new system:{(dy(t)/dt)=-cy(t)+(kαx2(t)y(t)/x2(t)+β2).(dx(t)/dt)=ax(t)-bx2(t)-(αx2(t)y(t)/x2(t)+β2),}t≠nT,{Δy(t)=-p2y(t)+q.Δx(t)=-p1x(t),}t=nT.When q>0,0 ≤ p1<1 and 0 ≤ p2<1,we obtain conditions for global asymptotic stability of pest-eradication periodic solution and permanence of the new system,and also obtain the existence of a postive periodic solution of the new system.Finally,we discuss the existence and stability of the predator-free periodic solution. |
| Key words: functional response of Holling type Ⅲ impulsive effect globally asymptotical stability permanence bifurcation |
