THE OPTIMAL CONTROL PATTERN OF OASIS HELTERFOREST SYSTEM AND ITS APPLICATION
Received date: 2001-07-30
Revised date: 2001-10-30
Online published: 2002-02-01
In this paper, we take the oasis shelterforest system in Hexi as the research object, analyze the spacetime feature of the distribution of forest resources of shelterforest 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，umin≤u（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 twodimension optimal control model of multiresources population is:
State equation: dxi/dt=rixi（1-xi/ki）-kiExi，（i=1，2）
Restrictive condition：xi≥0，（i=1，2），Emin≤E≤Emax
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' breasthigh diameter is k/2=18.22 cm. We also calculate the optimal control variables of breast high diameter under different costprice 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.
LI Zizhen，CHENG Guodong，HUI Cang . THE OPTIMAL CONTROL PATTERN OF OASIS HELTERFOREST SYSTEM AND ITS APPLICATION[J]. Advances in Earth Science, 2002 , 17(1) : 27 -32 . DOI: 10.11867/j.issn.1001-8166.2002.01.0027
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