Abstract: In recent years, much attention has been payed to desertification in Xinjiang, China ,there are many researches about desertification in different research areas and have achieved significant results, but there are few studies about desertification in differential equation area, especially in China. In this paper the interaction between sandy land and spares vegetation in oasis-desert eco-tone was analyzed and based on the analysis, a mathematical model for predictive desertification was presented and verified using Minfeng oasis as an example .The Runge-Kutta scheme was applied to the model. Dynamic changes of sandy land were conducted using remote sensing technology, and the trend of desertification was predicted with the mathematical model. The result was fairly rational.The model is simple and very useful in predicting and managing desertification.

摘要： 近年来,沙漠化问题日益受到关注,虽然各学科有关沙漠化的研究很多,也取得了显著的成果,但是在微分方程领域中有关沙漠化的研究却相对很少,在国内几乎空白.通过讨论绿洲-沙漠交错带中沙漠与绿洲之间的相互作用关系,参考传染病模型,根据数学物理原理建立了沙漠扩散预测模型,最后以民丰县为例验证了模型的正确性.利用龙格-库塔方法对数学模型进行了数值模拟,并与遥感图像处理技术相结合对民丰县绿洲进行了沙漠动态变化分析与预测,得到了较理想的结果,预测得到的结果与实际数据之间的偏差合理.提出的数学模型简单且实用,在预测和治理沙漠扩散工作中具有较大意义.