| 脉冲喷洒杀虫剂的植物病害模型的周期解 |
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| 引用本文： | 高贝贝,王定江.脉冲喷洒杀虫剂的植物病害模型的周期解[J].应用泛函分析学报,2014(4):303-307. |
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| 作者姓名： | 高贝贝 王定江 |
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| 作者单位： | 浙江工业大学理学院,杭州310023 |
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| 基金项目： | 国家自然科学基金（61273016）;浙江省自然科学基金（Y6100611） |
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| 摘 要： | 本文研究脉冲喷洒杀虫剂的植物病害模型.考虑在传染率随时间周期变化和森林树木总数保持不变的条件下,讨论具有垂直传播的一类具有单个种群的脉冲喷洒农药的SIRS模型,根据单值算子和Bohl-Brouaser不动点理论证明了无病周期解存在性,并且利用单值矩阵,Floquet理论得到其基本再生数并且给出了其无病周期解局部渐近稳定的条件.
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| 关 键 词： | 脉冲喷洒农药 植物病害模型 无病周期解 稳定性 |
Periodic Solution of the Plants Diseases Model with Impulsive Spraying Insecticide |
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| GAO Beibei,WANG Dingjiang.Periodic Solution of the Plants Diseases Model with Impulsive Spraying Insecticide[J].Acta Analysis Functionalis Applicata,2014(4):303-307. |
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| Authors: | GAO Beibei WANG Dingjiang |
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| Institution: | (College of Science, Zhejiang University of Technology, Hangzhou 310023, China) |
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| Abstract: | Considering that the infection rate evolves periodically with time and the total numberof forest trees remain unchanged, we dicuss the SIRS model of impulsive spraying pesticide with vertical transmission and single species. Firstly, according to ＇the Monodromy operator and Bohl- Brouaser fixed point theory＇, we demonstrate the existence of a disease-free periodic solution of thesystem. Secondly, taking advantage of ＇Monodromy matrix and Floquet theory＇, we obtain a basic reproductive rate of the model. Lastly, we work out the conditions of locally asymptotic stability of disease-free periodic solution of the model. |
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| Keywords: | impulsive the plants diseases the periodic solution stability |
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