多斑块上年龄结构种群模型的持久性分析
Persistence analysis of the age-structured population model on several patches
摘要：
我们考虑一个非线性偏微分方程系统，它描述了一个年龄结构的人口生活在变化的环境中的$N$补丁。我们证明了解的存在性和唯一性，并分析了系统的大时间行为的时间无关的情况下，周期变化和不规则变化的环境。在假设每一个斑块都可以从其它斑块直接到达或通过若干个中间斑块到达，且净再生算子的谱半径大于1的条件下，证明了种群在所有斑块上都是持久的.如果谱半径小于或等于1，则所有斑块上的消光即将发生。
英文摘要：
We consider a system of nonlinear partial differential equations that describes an age-structured population living in changing environment on $N$ patches. We prove existence and uniqueness of solution and analyze large time behavior of the system in time-independent case, for periodically changing and for irregularly varying environment. Under the assumption that every patch can be reached from every other patch, directly or through several intermediary patches, and that net reproductive operator has spectral radius larger than one, we prove that population is persistent on all patches. If the spectral radius is less or equal one, extinction on all patches is imminent.
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