水体富营养化状态脉冲控制系统周期解的存在性和唯一性

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水体富营养化状态脉冲控制系统周期解的存在性和唯一性孙树林, 段晓祥山西师范大学数学与计算机科学学院, 临汾 041000 Existence and Uniqueness of Periodic Solution of a State-dependent Impulsive Control System on Water Eutrophication SUN Shulin, DUAN XiaoxiangSchool of Mathematics and Computer Science, Shanxi Normal University, Shanxi, Linfen 041000

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摘要本文基于藻类治理问题,建立了一个具有状态依赖脉冲和 Holling I 型功能性反应函数的藻类治理模型, 利用常微分方程的定性理论和 Lambert W函数以及 Poincare 映射的性质研究了系统阶1周期解的存在性和唯一性. 最后, 通过数值模拟对文中主要结论进行了验证.

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收稿日期: 2014-12-15

PACS:

O175.14

基金资助:山西省自然科学基金(2013011002-2)资助项目.

引用本文:

孙树林, 段晓祥. 水体富营养化状态脉冲控制系统周期解的存在性和唯一性[J]. 应用数学学报, 2016, 39(1): 138-152. SUN Shulin, DUAN Xiaoxiang. Existence and Uniqueness of Periodic Solution of a State-dependent Impulsive Control System on Water Eutrophication. Acta Mathematicae Applicatae Sinica, 2016, 39(1): 138-152.

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