| 引用本文： |
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潘红卫,梁志清.一类具阶段结构的捕食系统正周期解的存在性[J].广西科学院学报,2007,23(1):13-17. [点击复制]
- PAN Hong-wei,LIANG Zhi-qing.Existence of Positive Periodic Solution for a Predator-prey System with Stage Structure[J].Journal of Guangxi Academy of Sciences,2007,23(1):13-17. [点击复制]
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| 摘要: |
建立具有阶段结构和自食现象而且食饵和捕食者均受密度制约的周期捕食系统:
⎛x'(t)=x(t)[β1(t)-a(t)x(t)]-b(t)x(t)z2(t),
⎜z'1(t)=β2(t)z2(t)-s(t)z1(t)-c(t)z1(t)z2(t),
⎨
⎜z'2(t)=r(t)z1(t)-d(t)z22(t)+e(t)z1(t)z2(t)+h(t)x(t)z2(t),
⎝x(0)>0,z1(0)>0,z2(0)>0,并且利用重合度理论得到正周期解存在的充分条件为dlsl > eMβ2M+(bM/β1l)(rMβ2M+(hMβ1Msl/al)). |
| 关键词: 捕食系统 阶段结构 自食 正周期解 重合度 |
| DOI： |
| 投稿时间：2006-06-28 |
| 基金项目: |
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| Existence of Positive Periodic Solution for a Predator-prey System with Stage Structure |
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PAN Hong-wei1, LIANG Zhi-qing2
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| (1.Quzhi Branch School of Guangxi Radio and TV University, Nanning, Guangxi, 530022, China;2.Department of Mathematics and Computer Science, Yulin Normal University, Yulin, Guangxi, 537000, China) |
| Abstract: |
In this paper,a class of predator-prey system with stage structure and cannibalism is established,which is restricted by prey's and predators' density:
⎛x'(t)=x(t)[β1(t)-a(t)x(t)]-b(t)x(t)z2(t),
⎜z'1(t)=β2(t)z2(t)-s(t)z1(t)-c(t)z1(t)z2(t),
⎨
⎜z'2(t)=r(t)z1(t)-d(t)z22(t)+e(t)z1(t)z2(t)+h(t)x(t)z2(t),
⎝x(0)>0,z1(0)>0,z2(0)>0.
By means of the theory of coincidence degree,a sufficien condition is obtained for the existence of positive periodic solution:dlsl > eMβ2M+(bM/β1l)(rMβ2M+(hMβ1Msl/al)). |
| Key words: predator-prey system stage structure cannibalism positive periodic solution coincidence degree |
