非自治Lotka-Volterra型捕食扩散系统中有害时滞对该系统持久性的影响(英文)

Profitless Delays for Permanence in Nonautomous Lotka-Volterra Predator-Prey Dispersal Systems

研究了时滞对一类非自治Lotka-Volterra型捕食扩散系统的影响,该系统由n个斑块组成,食饵种群可以在斑块间迁移,而捕食者限制在某一个斑块不能扩散.我们假设密度制约项系数并不总是严格正的.通过运用比较定理及时滞泛函微分方程的基本原理,分两种情况表明了在一定条件下系统是一致持久的.两种情况的结果表明时滞的引入和变化即可能是"有害",也可能是"无害".进一步还说明了系统在一致持久性的条件下至少存在一个正周期解.这些结果是对已知的非自治Lotka-Volterra系统的一些结果的推广与改进.

This paper studies the effect of time delays on a nonautonomous Lotka- Volterra predator-prey dispersal system which consists of n-patches, the prey species can disperse among n-patches, but the predator species is confined to one patch and cannot disperse. We study the delayed Lotka-Volterra system where the coefficients of dependent density terms are not always strictly positive. By using comparison theorem and delays functional differential equation basic theory, we show that the system is uniformly persistent under some appropriate conditions in two cases. Our results suggest that under some conditions, the introduction and the variance of the time delays can be both harmless and profitless, Further, by using fixed point theorem, we obtain that there is at least a positive periodic solution under conditions for the permanence of system. These results are basically an extension and improvement of the known results for nonautonomous Lotka-Volterra systems.