| 摘要: |
| 重访一3维阶段构造模型，它的两种群持久和一种群或者两种群灭绝的必要充分条件先前已经得到.通过使用中心流型定理，证明这个系统的非负平衡点在临界状态a=b+ce时也是局部渐近稳定的.主要新的发现是:系统中与有限动力学无关的参数d在系统的无穷远动力学中担任一个关键角色.更具体地，通过在R3中使用庞加莱紧性法，对该模型的性质做了一个全局分析，包括在无穷远球面上动力学的完整描述.组合解析与数值的技术,证明了在参数满足a≤ b且0<d<1的条件下，系统具有两条无穷远异宿轨. |
| 关键词: 阶段结构捕食模型 中心流型定理 无穷远动力学 庞加莱紧性法 无穷异宿轨 |
| DOI：10.3969/J.ISSN.100-5137.2017.03.011 |
| 分类号: |
| 基金项目:This research was supported by the Natural Science Foundation (NSF) of Zhejiang Province (No. LQ13A01 0019);NSF of China (No. 61473340);NSF of Zhejiang University of Science and Technology (No. F701108G14) |
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| Some new observations for a stage-structured predator-prey model |
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Li Wei, Li Xianyi
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Department of Big Data Science, College of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China
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| Abstract: |
| A 3D stage-structured predator-prey model, whose necessary and sufficient conditions for the permanence of two species and the extinction of one species or two species were previously obtained, is revisited in this paper. By using the center manifold theorem, we show that the nonnegative equilibrium point of this system is also locally asymptotically stable in the critical case a = b + ce. Our main new discovery is that the parameter d in this model irrelevant to finite dynamical behaviors of this system plays a role in the dynamical behaviors at infinity of this system. More specially, by using the Poincaré compactication in R3 we make a global analysis for this model, including the complete description of its dynamic behavior on the sphere at infinity. Combining analytical and numerical techniques we show that for the parameters satisfying a ≤ b and 0 < d < 1, the system presents two infinite heteroclinic orbits. |
| Key words: stage-structured predator-prey model center manifold theorem dynamics at infinity Poincaré compactification infinite heteroclinic orbit |
