具有单个反馈控制变量的非自治差分两种群竞争系统的持久性和全局吸引性  

Permanence and Global Attractivity of a Nonautonomous Discrete Two Species Competitive System with Single Feedback Control

作　　者：王丹红[1] 

机构地区：[1]闽江学院数学系,福州350108

出　　处：《工程数学学报》2015年第3期425-431,共7页Chinese Journal of Engineering Mathematics

基　　金：福建省自然科学基金(2012J05007)~~

摘　　要：从环境保护的角度看,持久性和稳定性是生态系统非常重要的性质,而外界因素对生态系统的干扰是不可避免的,所以研究反馈控制下生态系统的稳定性具有较大的理论意义.本文提出一类具有单个反馈控制变量的非自治差分两种群竞争系统,并利用比较原理和微分中值定理,得到了保证系统持久和全局吸引的充分条件.最后,通过数值模拟验证了所得结论的可行性.From the perspective of environmental protection, the permanence and stability are important characteristics of ecosystems. However, it is inevitable that external factors have influence on ecosystems, so it is important for us to study theoretically the stability of an ecosystem under the condition of feedback control. In this paper, we firstly propose a nonautonomous discrete Lotl^-Volterra competitive system with a single feedback control. Furthermore, by utilizing the standard comparison theorem and the differential mean value theorem, we obtain the sufficient conditions for the permanence and global attractivity of the system. Finally, a numerical example shows the feasibility of our main results.

关 键 词：非自治差分 反馈控制 竞争系统 持久性 全局吸引性 

分 类 号：O175.14[理学—数学]