时变斑块上年龄结构种群模型的持久性
Permanency of the age-structured population model on several temporally variable 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居住在几个随时间变化的补丁。我们证明了解的存在性和唯一性，并分析了它的大时间行为的情况下，当环境是恒定的，当它的周期变化。一个关键的假设是，个人可以分散，每个补丁可以从其他补丁，直接或通过几个中间补丁到达。引入了非时变周期模型的净再生算子和特征方程，证明了系统的持久性由净再生率定义。如果净繁殖率小于或等于1，则所有斑块的灭绝迫在眉睫。否则，保证所有补丁的永久性。证明是基于一种新的方法来分析大时间的稳定性。
英文摘要：
We consider a system of nonlinear partial differential equations that describes an age-structured population inhabiting several temporally varying patches. We prove existence and uniqueness of solution and analyze its large-time behavior in cases when the environment is constant and when it changes periodically. A pivotal assumption is that individuals can disperse and that each patch can be reached from every other patch, directly or through several intermediary patches. We introduce the net reproductive operator and characteristic equations for time-independent and periodical models and prove that permanency is defined by the net reproductive rate for the whole system. If the net reproductive rate is less or equal to one, extinction on all patches is imminent. Otherwise, permanency on all patches is guaranteed. The proof is based on a new approach to analysis of large-time stability.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
