Logistic种群收获模型

Logistic种群收获模型

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Contributor

contributed at 2018-12-04

Authorship

Affiliation:  
岳天祥编著
Email:  
yue@lreis.ac.cn
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Method-focused categoriesProcess-perspectiveBiological process calculation

Detailed Description

Chinese {{currentDetailLanguage}} Chinese

Logistic种群收获模型

    1)收获时的种群系统可以由下面的方程描述:

式中,是系统的个体数;t是时间;k是一个正常数;u是一个未知的非负控制变量。

收获的生态和经济成本由下面的函数描述:

式中,是一个非负值的关于的未知函数;c是一个已知正常数。

2)定义一个Liapunov函数:

的变化率为:

3)根据最佳稳定性理论,我们建立了下面的表达式:

4)根据Krasovskii的最佳稳定性定理,当时,表达式达到最小值0,最优化控制满足方程:

一种解法为:

未知函数为:

成本函数变为:

 

 

参考文献

    Gopalsamy Klogistic种群模型中的最优稳定性和收获。Ecological Modelling198011

How to Cite

《资源环境数学模型手册》 (2018). Logistic种群收获模型, Model Item, OpenGMS, https://geomodeling.njnu.edu.cn/modelItem/980f0557-857a-4412-ac44-1fed0c449987
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History

Last modifier : 
Kai Wu
Last modify time : 
2020-12-02
Modify times : 
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Contributor

contributed at 2018-12-04

Authorship

Affiliation:  
岳天祥编著
Email:  
yue@lreis.ac.cn
Homepage:  
View
Is authorship not correct? Feedback

History

Last modifier : 
Kai Wu
Last modify time : 
2020-12-02
Modify times : 
View History

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