对“一类带收获率的离散时滞人口模型正周期解存在性”的探究

Exploration about the Existence of Positive Periodic Solutions for a Class of Discrete Time Delayed Population Model with Harvesting Rate

本文对一类带收获率的离散时滞人口模型正周期解的存在性进行了探究.以迭合度理论中的延拓定理为理论基础,通过分析变形、利用一些不等式估计技巧构造了两个有界开集,再利用Brouwer度的同伦不变性,我们计算得知在这两个有界开集中算子的Brouwer度不等于零,从而得到了这类离散模型两个正周期解存在的充分条件.最后,举出两个例子来验证我们的主要结论,并提出了有待进一步解决的问题.

This paper aims at the existence of positive periodic solutions for a class of discrete time delay population model with harvesting rate. The discreted system represents many population models and is very worth to research. The whole article is divided into three parts to elaborate. In the second part, by means of a continuous theorem of Brouwer coincidence degree theory, through the analysis of deformation and use some estimation of inequality technique, we construct two bounded open sets. At the same time, by using the homotopy invariance , we have calculated to explain that the Brouwer degree of the two open bounded operator is not equal to zero. So we have got the sufficient conditions to the system＇s two positive periodic solutions. In the third part, two examples are given to verify our main conclusions. And we put forward the problems to be further studied.