1. 1.兰州大学数学系，甘肃 兰州 730000；2.中国科学院寒区旱区环境与工程研究所，甘肃 兰州 730000；3.兰州大学干旱农业生态国家重点实验室，甘肃 兰州 730000
• 收稿日期:2001-07-30 修回日期:2001-10-30 出版日期:2002-12-20
• 通讯作者: 李自珍（1944-），男，河南省许昌市人，教授，主要从事数量生态学方向的研究工作.E-mail:zizhen Li@sohu.com E-mail:zizhen Li@sohu.com
• 基金资助:

中科院知识创新工程重大项目（编号：KZCX1-09）；国家自然科学基金项目“沙漠植物生态位构建与生活史对策研究”（编号：39970135）；荒漠区人工自然景观空间格局及其生态风险分析（编号：30070139）资助.

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

LI Zizhen 1，CHENG Guodong 2，HUI Cang 3

1. 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:2001-07-30 Revised:2001-10-30 Online:2002-12-20 Published:2002-02-01

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.

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