| 基于蓝藻水华控制的脉冲微分方程模型 |
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| 引用本文： | 徐为坚,陈兰荪.基于蓝藻水华控制的脉冲微分方程模型[J].广西科学,2008,15(1):10-13. |
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| 作者姓名： | 徐为坚 陈兰荪 |
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| 作者单位： | 1. 玉林师范学院数学与计算机科学系,广西玉林,537000
2. 中国科学院数学与系统科学研究院,北京,100080 |
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| 基金项目： | 国家自然科学基金项目(10471117)，广西教育厅科研项目(200707LX143)资助 |
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| 摘 要： | 根据藻类生长特点,以具有饱和反应增长率的非自治增长模型为基础,采用分次脉冲喷洒的方法建立蓝藻脉冲控制模型,并将模型转化为脉冲微分系统,给出确定系统最大脉冲周期的方法,并用数值例子说明如何在有限时间内,选择适当的杀藻剂和脉冲喷洒次数,将蓝藻种群的密度控制在经济阈值之下.
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| 关 键 词： | 微分方程 边值问题 蓝藻 |
| 文章编号： | 1005-9164(2008)01-0010-04 |
| 收稿时间： | 2007/8/27 0:00:00 |
| 修稿时间： | 2007年8月27日 |
Impulsive Differential Equation Model Based on Controlling Cyanobacteria Bloom |
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| XU Wei-jian and CHEN Lan-sun.Impulsive Differential Equation Model Based on Controlling Cyanobacteria Bloom[J].Guangxi Sciences,2008,15(1):10-13. |
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| Authors: | XU Wei-jian and CHEN Lan-sun |
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| Institution: | Department of Mathematics and Computer Science, Yulin Normal University, Yulin, Guangxi, 537000, China and Institute of Mathematics, Academy of Mathematics and System Sciences, Beijing, 100080, China |
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| Abstract: | According to the growth characteristics of algae and based on the non-autonomous growth model with saturated reaction increasing rate, this paper constructs the impulsive control model of cyanobacteria using the method of separately impulsive spraying,and then transforms the model into the impulsive differential system.Furthermore,this paper presents the method of determining the maximum pulse period of the system,and makes use of the numerical simulations to illustrate how to select the algaecide and the times of impulsive spraying in a finite time for controlling the density of the cyanobacteria population to be lower than the economic threshold. |
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| Keywords: | differential equation boundary value problem cyanobacteria bloom |
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