绿洲-沙漠交错带沙漠扩散预测模型的改进

摘要

近年来,沙漠化问题日益受到关注,虽然各科学有关沙漠化的研究较多,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.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,根据前人提出的非线性项为乘积形式的沙漠扩散预测模型的基础上建立了新的非线性项为比例依赖函数的沙漠化预测模型,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,预测得到的结果比前人得到的结果好,与实际数据之间的偏差更合理.提出的数学模型简单且实用,进一步更好地反映了研究区域的环境变化,在预测和治理沙漠扩散工作中具有较大意义.%Resently,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 different 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 previous desert prediction model,a new ratio-dependent functional desert prediction model is established,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.