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THE OPTIMAL CONTROL PATTERN OF OASIS HELTERFOREST SYSTEM AND ITS APPLICATION

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  • 1.Department of Mathematics, Lanzhou University, Lanzhou 730000,China; 2.Cold and Arid Regions Environmental and Engineering Research Institute, CAS, Lanzhou 730000,China; 3.State Key Laboratory of  Arid Agroecology, Lanzhou University, Lanzhou 730000,China

Received date: 2001-07-30

  Revised date: 2001-10-30

  Online published: 2002-02-01

Abstract

In this paper, we take the oasis shelterforest system in Hexi as the research object, analyze the spacetime feature of the distribution of forest resources of shelterforest and the growth dynamic of established populations. By using the theory of biological control, we construct the maximum sustainable output model of the biological resources management, the optimal control model under the meaning of ecological economics, and the control model of multi resource populations. 
 The optimal control model in perspective of ecological economy is:
  State equation: dx/dt=rx(1-x/k)-u(t)  Restrictive condition:x≥ k/2,uminu(t)≤umax
  Target function: J(u)=∫+∝0e-δt(P-C(x))u(t)dt
 Here is the resource population size;  dx/dt represents the growth rate of population; r and  k are intrinsic rate of increase and carrying capacity, respectively;  is control variable; and others are model coefficients.
 The twodimension optimal control model of multiresources population is:
State equation: dxi/dt=rixi1-xi/ki-kiExi,(i=1,2)
Restrictive condition:xi0,(i=1,2),EminEEmax
Target function: J(E)=∫+∞0e-δt[P1k1x1+P2k2x2-C]E(t)dt
 Where  xi and dxi /dt are, respectively, the size and growth rate of the resource population ; i; ri and  ki are its intrinsic growth rate and carrying capacity, E=E(t) respectively; represents the combine control variable.
Based on observation and experiments, the criteria of resource protection and the optimal population level and the measure of artificial regulation are given. The protection index of Populus gansuensis' breasthigh diameter is k/2=18.22 cm. We also calculate the optimal control variables of breast high diameter under different costprice ratio. Furthermore, the ecological water requirement of oasis shelter forest and the strategy sustainable development are proposed, in which the ecological required water quantity of crop field is 1 796 m3/hm2and the one of sand fixation and sand prevention woods is 57 100 m3/hm2.

Cite this article

LI Zizhen,CHENG Guodong,HUI Cang . THE OPTIMAL CONTROL PATTERN OF OASIS HELTERFOREST SYSTEM AND ITS APPLICATION[J]. Advances in Earth Science, 2002 , 17(1) : 27 -32 . DOI: 10.11867/j.issn.1001-8166.2002.01.0027

References

[1] Levin S A, Hallam T G, Gross L J. Applied Mathematical Ecology [M]. Berlin: Springer-Verlag, 1994. 3-81.
[2] Clark C W, Clark F. The optimal exploitation of renewable resource stocks: problems of irreversible investment [J]. Econometrica, 1979, 47: 25-49.
[3] Eswaran M, Lewis T R. Ultimate recovery of an exhaustible resource under different market structures [J]. J Environ Econ Manag, 1984, 11: 55-69.
[4] Mckelvey R. Decentralized regulation of a common property resource industry with irreversible investment [J]. J Environ Econ Manag, 1985, 12: 287-307.
[5] Clark C W. Mathematical Biological Economy [M]. Shenyang: Northeast Agriculture Press, 1984 (Translated by Zhou Q X, Qiu F Z). [克拉克 C W著.数学生物经济学 [M]. 周勤学,丘兆福译. 沈阳: 东北农业出版社, 1984.]
[6] Smith J M. Ecological Model [M]. Lang Xin trans. Beijing: Science press, 1979 . [史密斯 J M.生态学模型 [M]. 朗新译. 北京:科学出版社,1979.]
[7] Northeast Forestry College. Forestry Ecology [M]. Beijing: Chinese Forestry Press, 1981. [东北林学院主编. 森林生态学 [M]. 北京:中国林业出版社,1981.]
[8] Chen Qingcheng. The investigation of some mountain plant's modality and ecological traits in east Qilian mountain at Gansu Province [J]. Selective Paper of Plant Ecology and Ground Botany, 1966. [陈庆诚. 甘肃省祁连山东段一些高山植物的形态与生态学特征的观察 [J]. 植物生态学与地植物学丛刊, 1966.]
[9] Li Zizhen, Liu Xiaoping, Jiang Wenlan. Research on optimal stocking system pattern of artificial grassland [J]. Actaprataculturae Sinica, 1998, 4: 61-66. [李自珍, 刘小平, 蒋文兰. 人工草地放牧系统优化模式研究 [J]. 草业学报, 1998, 4: 61-66.]
[10] Li Zizhen. Discussion on optimal control pattern of mixture artificial grassland stocking system [J]. Journal of Lanzhou University (Special), 2000, 36: 98-102. [李自珍. 混播人工草地放牧系统最优控制模式探讨 [J]. 兰州大学学报(专辑), 2000, 36: 98-102.]
[11] Feng Jinchao, Liu Xinmin. The Relationship between Arid Environment and Plant Water [M]. Beijing: Chinese Environmental Science Press, 1998.[冯金朝, 刘新民. 干旱环境与植物水分关系 [M]. 北京: 中国环境科学出版社, 1998.]
[12] Fan Shengyue. Development Strategies and Key Technology of Sand Industry in Zhangye Region [M]. Beijing: Chinese Environmental Science Press, 1998.7. [樊胜岳. 张掖地区沙产业发展对策与关键技术 [M]. 北京: 中国环境科学出版社, 1998.7.]

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