一类具年龄结构n维食物链模型的最优收获控制

雒志学; 杜明银

一类具年龄结构n维食物链模型的最优收获控制

雒志学^1,2,
杜明银¹

1.
兰州交通大学数学系,兰州 730070;2.杭州电子科技大学理学院,杭州 310018

基金项目: 国家自然科学基金资助项目(10771048)

详细信息

作者简介:
雒志学(1963- ),男,甘肃宁县人,博士,副教授(联系人.Tel:+86-931-4956559;E-mail:luozhix@263.net).

中图分类号: O175.1
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出版历程
- 收稿日期: 2007-09-02
- 修回日期: 2008-03-18
- 刊出日期: 2008-05-15

Optimal Harvesting for an Age-Dependent n-Dimensional Food Chain Model

LUO Zhi-xue^1,2,
DU Ming-yin¹

1.
Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, P. R. China;

摘要

摘要: 研究一类具有年龄结构n维食物链模型的最优收获控制．利用不动点定理，证明了系统非负解的存在性和唯一性．由Mazur定理，证明了最优控制策略的存在性，同时由法锥概念的特征刻画,还得到了控制问题最优解存在的必要条件．
- 食物链 /
- 年龄结构 /
- 最优控制 /
- 最大值原理
Abstract: Optimal harvesting policy for an age-dependent n-dimensional food chain model is studied.The existence and uniqueness of non-negative solution of the system were proved using the fixed point theorem.By Mazur's theorem,the existence of optimal control strategy was demonstrated and optimality conditions were derived by means of normal cone.
- food chain /
- age-dependence /
- optimal control /
- the maximum principle

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参考文献(16)

[1]	Brokate M.Pontryagin's principle for control problems in age-dependent population dynamics[J].J Math Biol,1985,23:75-101. doi: 10.1007/BF00276559
[2]	Murphy L F,Smith S J.Optimal harvesting of an age-structured population[J].J Math Biol,1990,29:77-90.
[3]	Clark C W.Mathematical Bioeconomics: the Optimal Management of Renewable Resouces[M].2Ed.New York:John Wiley and Sons Inc,1990.
[4]	Busoni G,Matucci S.A problem of optimal harvesting policy in two-stage age-dependent population[J].Math Biosci,1997,143:1-33. doi: 10.1016/S0025-5564(97)00011-4
[5]	Anita S.Optimal harvesting for a nonlinear age-dependent population dynamics[J].J Math Anal Appl,1998,226:6-22. doi: 10.1006/jmaa.1998.6064
[6]	Anita S,Iannelli M,Kim M Y,et al.Optimal harvesting for periodic age-dependent population dynamics[J].SIAM J Appl Math,1998,58(5):1648-1666. doi: 10.1137/S0036139996301180
[7]	Anita S.Analysis and Control of Age-Dependent Population Dynamics[M].Dordrecht:Kluwer Academic Publishers,2000.
[8]	Albrecht F,Gatzke H,Haddad A,et al.On the control of certain interacting populations[J].J Math Anal Appl,1976,53:578-603. doi: 10.1016/0022-247X(76)90094-9
[9]	Lenhart S,Liang M,Protopopescu V.Optimal control of boundary habitat hostility for interacting species[J].Math Mech Appl Sci,1999,22:1061-1077. doi: 10.1002/(SICI)1099-1476(19990910)22:13<1061::AID-MMA70>3.0.CO;2-I
[10]	Crespo L G,Sun J Q.Optimal control of populations of competing species[J].Nonlinear Dynamics,2002,27:197-210. doi: 10.1023/A:1014258302180
[11]	MENG Xin-zhu,JIAO Jian-jun,CHEN Lan-sun.The dynamics of an age structured predator-prey model with disturbing pulse and time delays[J].Nonlinear Analysis: Real World Applications,2008,9(2):547-561. doi: 10.1016/j.nonrwa.2006.12.001
[12]	Chan W L,Guo B Z.Optimal birth control of population dynamics[J].J Math Anal Appl,1989,144:532-552. doi: 10.1016/0022-247X(89)90350-8
[13]	Webb G F.Theory of Nonlinear Age-dependent Population Dynamics[M].N Y:Marcel Dekker,1985.
[14]	Iannelli M.Mathematical Theory of Age-Structured Population Dynamics[M].Pisa:E Stampatori,1994.
[15]	Barbu V,Precupanu T.Convexity and Optimization in Banach Spaces[M].Dordrecht-Boston:D.Reidel Publishing Company,1986.
[16]	孟新柱，陈兰荪，宋治涛.一类新的含有垂直传染与脉冲免疫的时滞SEIR传染病模型的全局动力学行为[J].应用数学和力学，2007,28(9):1123-1134.

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一类具年龄结构n维食物链模型的最优收获控制

作者简介:
雒志学(1963- ),男,甘肃宁县人,博士,副教授(联系人.Tel:+86-931-4956559;E-mail:luozhix@263.net).

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Optimal Harvesting for an Age-Dependent n-Dimensional Food Chain Model

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一类具年龄结构n维食物链模型的最优收获控制

作者简介: 雒志学(1963- ),男,甘肃宁县人,博士,副教授(联系人.Tel:+86-931-4956559;E-mail:luozhix@263.net).

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出版历程

Optimal Harvesting for an Age-Dependent n-Dimensional Food Chain Model

计量

出版历程

目录

作者简介:
雒志学(1963- ),男,甘肃宁县人,博士,副教授(联系人.Tel:+86-931-4956559;E-mail:luozhix@263.net).