PERSISTENCE IN INFINITE-DIMENSIONAL SYSTEMS
PERSISTENCE IN INFINITE-DIMENSIONAL SYSTEMS
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DOI：
10.1137/0520025
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发表时间：
1989-03-01
影响因子：
2
通讯作者：
WALTMAN, P
中科院分区：
文献类型：
--
作者：
HALE, JK;WALTMAN, P
持续性的概念反映了模型生态系统的所有组成部分的生存。到目前为止，大多数结果仅限于常微分方程式或局部紧空间上的动力学。本文在渐近光滑的a-半群的背景下研究了这一概念。由于种群动力学方程往往涉及延迟或扩散，这似乎是适当的设定。在边界上的流动上设置了条件，如果存在耗散性和渐近光滑性假设所提供的全局吸引子，则这些条件是持续生存的必要条件和充分条件。
The concept of persistence reflects the survival of all components of a model ecosystem. Most of the results to date are restricted to ordinary differential equations or to dynamics on locally compact spaces. The concept is investigated here in the setting of a-semigroup which is asymptotically smooth. Since the equations of population dynamics often involve delays or diffusion this seems the appropriate setting. Conditions are placed on the flow on the boundary which, given the presence of a global attractor provided by the assumption of dissipativeness and asymptotic smoothness, are necessary and sufficient for persistence.