一类时滞四种群食物链生态模型的渐近性态  

Asymptotic Behavior of Solutions for a Four-Specie Food Chain Ecological Model with Time Delays

作　　者：苗宝军[1] 周伦[1] 容跃堂[2] 

机构地区：[1]许昌学院数学科学学院,河南许昌461000 [2]西安工程大学理学院,陕西西安710048

出　　处：《许昌学院学报》2008年第2期4-8,共5页Journal of Xuchang University

基　　金：河南省科技厅自然科学基金项目(0611055100);河南省教育厅自然科学基础研究项目(2006120006)

摘　　要：利用解的整体存在性定理、上下解方法和相应的单调迭代序列,研究了一类在有界区域上具有牛曼边界条件的时滞四种群食物链反应扩散模型,给出了简单和易验证的解的存在性和平衡态方程正解的全局渐近稳定性的充分条件.这个结果隐含着食物链系统的共存是持久的,平凡解和所有半平凡解是不稳定的.In this paper, by means of the theory of global existence and upper-lower solutions methods and the associated monotone iterations, a four-specie food chain model for reaction diffusion systems in a bounded do-main with time delays and Neumann boundary condition problem is investigated, and a simple and easily verifiable sufficient condition for the existence of solutions and global asymptotic stability of a positive steady-state solution are given. The result implies that the coexistence of food-chain system is permanent, and the trivial and all forms of semitrivial solutions are unstable.

关 键 词：反应扩散模型 全局渐近稳定性 食物链 时滞 上下解 

分 类 号：O175.29[理学—数学]