一类具有外加毒素的非均匀恒化器模型分析

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一类具有外加毒素的非均匀恒化器模型分析贾婷婷, 聂华, 张瑜陕西师范大学数学与信息科学学院, 西安 710119 The Analysis of the Unstirred Chemostat Model with External Toxin JIA Tingting, NIE Hua, ZHANG YuCollege of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119, China

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摘要研究了一类具有外加毒素的非均匀恒化器模型.毒素的引入破坏了系统生物量守恒定律，使系统不能降维，从而导致模型成为一类具有捕食与竞争结构的非单调系统.首先，采用度理论和线性稳定性理论研究了半平凡解的存在唯一性及其渐近性态.其次，运用度理论和分歧理论研究了系统正解的存在性，并分析了正解分支的结构.最后，从数值上验证并拓展了本文的理论结果.结果表明外加毒素存在时两物种可以共存于平衡点或者极限环.

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收稿日期: 2015-10-19

PACS:

O175.26

基金资助:国家自然科学基金（11671243），陕西省青年科技新星计划（2015KJXX-21），陕西省自然科学基础研究计划（2014JM1003），中央高校基本科研业务费专项资金（GK201701001，GK201302005）资助项目.

引用本文:

贾婷婷, 聂华, 张瑜. 一类具有外加毒素的非均匀恒化器模型分析[J]. 应用数学学报, 2017, 40(3): 377-399. JIA Tingting, NIE Hua, ZHANG Yu. The Analysis of the Unstirred Chemostat Model with External Toxin. Acta Mathematicae Applicatae Sinica, 2017, 40(3): 377-399.

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