基于生态环境和反馈控制的多种群竞争系统的正周期解

Positive Periodic Solution of Multiple Species Comptition System with Ecological Environment and Feedback Controls

根据种群动力学原理建立了基于生态环境和反馈控制的时滞非自治Lotka-Volterra多种群竞争系统,并在反馈控制变量的构造上采用了高次非线性函数形式.利用重合度理论中Gaines和Mawhin延拓定理,给出了该系统的正周期解存在性的充分条件.利用Barbalat引理以及构造适当的Lyapunov函数。

In this paper, by using species dynamic theory, a delay nonautonomous Lotka- Volterra multiple species competition system with ecological environment and feedback controls is established, and the high order nonlinear function is used in the construction of the feedback control variables. By using Continuation Theorem based on Gaines and Mawhin＇s coincidence degree theory, the sufficient conditions for existence of positive periodic solution of the system are obtained. Using Barbalat Lemma and constructing an appropriate Lyapunov function, the algebraic criterion for the uniqueness and global attractivity of positive periodic solutions of the system are obtained.