绿洲防护林系统的最优控制模式及其应用研究

以河西地区绿洲防护林系统为研究对象，分析了防护林资源分布的时空特征及建群种的增长动态，运用生物控制理论，构建了防护林区生物资源管理的最大持续产量模型、生态经济意义下的最优控制模型及多资源种群控制模型。根据有关模型和试验观测结果，确定了防护林建群种的资源保护指标、生态经济意义下的最优种群水平和人工调控措施。该防护林主要建群种二白杨胸径的保护指标为 k/2＝18．22cm，在不同成本与价格比下计算了主要建群种二白杨胸径指标的个最优控制量。估算了防护林系统的生态需水量，其中农田生态需水量为 1 796 m³/hm²，固沙林和阻沙防护林生态需水量为57 100m³/hm²，并提出了相应的持续发展对策。

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

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，u_min≤u（t）≤u_max；
  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: dx_i/dt=r_ix_i（1-x_i/k_i）-k_iEx_i，（i=1，2）
Restrictive condition：x_i≥0，（i=1，2），E_min≤E≤E_max
Target function: J（E）=∫^+∞₀e^-δtP₁k₁x₁+P₂k₂x₂-C］E（t）dt
 Where  x_i and dx_i /dt are, respectively, the size and growth rate of the resource population ; i; r_i and  k_i 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.