多板块水-植物模型的随机性及其土壤沙漠化改善策略

Randomicity of multi-plate water-plant model and strategies for improving soil desertification

为了改善科尔沁沙地土壤荒漠化的问题,通过改进水-植物的数学模型研究影响水的扩散因素及其对植物生长的影响.基于马尔科夫链,通过借助Kolmogorov方程计算得出水量的概率密度函数.将水-植物模型应用到多板块水的扩散问题中,利用全期望公式计算出某时刻水量的期望值,讨论极限期望得出水成功地扩散到四周植物的条件.分析结果表明,当降水量去除蒸发项大于向四周的植物扩散的水分时,植物能够正常存活及生长;降水量去除蒸发项小于向四周的植物扩散的水分时,表示该区域水分是有限的,无法向四周的植物提供充足的水分.分析结果为控制降水量和蒸发项的大小,解决土壤的荒漠化问题提供了理论支持.

In order to improve the problem of soil desertification in Horqin sandy land, the diffusion factors of water and their effects on plant growth are studied by improving the mathematical model of water-plant.Based on Markov chain, the probability density function of water volume is calculated by Kolmogorov equation.Then the water-plant model is applied to the diffusion problem of water in multiple plates, and the expectation of water amount at a certain moment is calculated by the full expectation formula.Furthermore,by discussing the limit expectation,obtains the conditions of water successful diffusion to the surrounding plants. The theoretical results reveal that when the evaporation term of precipitation is still larger than the water diffused to the surrounding plants, the plants can survive and grow normally,if the evaporation term of precipitation is less than the water diffused to the surrounding plants, it means that the water in this area is limited and there is no way to provide sufficient water to the surrounding plants.It provides theoretical support for controlling the amount of precipitation and evaporation to solve the desertification problem of soil.