| 一类时滞四种群食物链生态模型的渐近性态 |
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| 引用本文： | 苗宝军,;周伦,;容跃堂.一类时滞四种群食物链生态模型的渐近性态[J].许昌师专学报,2008(2):4-8. |
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| 作者姓名： | 苗宝军 ;周伦 ;容跃堂 |
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| 作者单位： | [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 |
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| 基金项目： | 基金项目：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）. |
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| 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-}生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。
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| 关 键 词： | 反应扩散模型 全局渐近稳定性 食物链 时滞 上下解 |
Asymptotic Behavior of Solutions for a Four-Specie Food ChainEcological Model with Time Delays |
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| Institution: | MIAO Bao-jun1,2 ,ZHOU Lun1 ,RONG Yue-tang2 ( 1. School of Mathematics Science, Xuchang University,Xuchang 461000, China;2. School of Science,Xi＇an Polytechnic University, Xi＇an 710048, China) |
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| Abstract: | 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. |
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| Keywords: | reaction-diffusion model global asymptotic stability food chain time delays upper and lowersolutions |
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