一类多偏差变元的n种群Lotka-Volterra模型的周期正解

On the Existence of Positive Periodic Solutions for n-Species Lotka-Volterra Population Model with Multiple Deviating Arguments

本文研究了一类多偏差变元Lotka-Volterra种群模型的间期正解问题,利用重合度拓展定理和一些分析技巧,得到了周期正解存在性的新结果.与已有文献相比,本文所讨论的模型更具一般性,它包含了以前人们所研究的竞争-种群模型、捕食-种群模型等,而且估计先验界的方法也是全新的.

In this paper, using some analysis techniques and the continuation theorem of coincidence degree theory, the authors study a kind of n-species Lotka-Volterra population model with multiple deviating arguments. Some new results on the existence of positive periodic solutions are obtained. For the comparision, the model subject to this paper is more general, which includes some known Lotka-Volterra type systems, such as competitive systems, predator-prey systems and so on. Meanwhile, the method to estimate a priori bounds of periodic solutions is different from the corresponding ones found in the existing literature.