UNIFORM PERSISTENCE AND PERIODIC COEXISTENCE STATES IN INFINITE-DIMENSIONAL PERIODIC SEMIFLOWS WITH APPLICATIONS
UNIFORM PERSISTENCE AND PERIODIC COEXISTENCE STATES IN INFINITE-DIMENSIONAL PERIODIC SEMIFLOWS WITH APPLICATIONS
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发表时间：
2005
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通讯作者：
Xiao-Qiang Zhao
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作者：
Xiao-Qiang Zhao
本文致力于研究无限维周期流的一致持久性和周期共存状态。在一般抽象条件下，证明了周期半流的一致持久性与其相应的Poincarb映射的一致持久性等价，并且证明了周期半流的一致持久性蕴含着周期共存状态的存在，推广和统一了已有的相关结果。作为应用，我们详细讨论了具有空间异质性的周期Kolmogorov捕食者-食饵反应扩散系统，得到了系统一致持续生存和全局灭绝的一些充分条件。
This paper is devoted to the study of uniform persistence and periodic coexistence states in infinite dimensional periodic eemiflows. Under a general abstract setting, we prove that the uniform persistence of a periodic semiflow is equivalent to that of its associated Poincarb map, and that the uniform persistence implies the existence of a periodic coexistence state, which generalizes and unifies some related earlier results. As an application, we discuss in detail the periodic Kolmogorov predator-prey reaction-diffusion system with spatial heterogeneity and obtain some sufficient conditions for the uniform persistence and global extinction of the system under consideration.