一类带有非局部作用和交叉扩散的植被模型的斑图动力学研究  

Pattern Dynamics of a Vegetation Model with Nonlocal Action and Cross Diffusion

作　　者：梁娟 郭尊光 杨焕青 张钧瑞 LIANG Juan;GUO Zun-guang;YANG Huan-qing;ZHANG Jun-rui(Department of Science,Taiyuan Institute of Technology,Taiyuan 030008,China;College of Resources and Environment,Shanxi University of Finance and Economics,Taiyuan 030006,China)

机构地区：[1]太原工业学院理学系,山西太原030008 [2]山西财经大学资源环境学院,山西太原030006

出　　处：《数学的实践与认识》2024年第1期99-104,共6页Mathematics in Practice and Theory

基　　金：山西省基础研究计划项目(202203021212327,202203021211213);太原工业学院青年(后备)学科带头人支持计划资助项目。

摘　　要：建立了带有非局部时滞和交叉扩散的植被—水模型,并且对在一维和二维空间上的非局部时滞项进行了详细的数学推导,从而将双变量的模型转化为三变量的反应扩散方程.通过数学分析,得到植被模型产生稳态斑图的条件通过数值模拟得到了植被斑图随时间的演替过程.结果表明,植被平均密度与交叉扩散系数呈正相关的关系,即随着交叉扩散系数的增加,植被平均密度会变大数值模拟结果较好地显示了交叉扩散系数对植被斑图的影响.A vegetation model with nonlocal delay and cross-diffusion is established,and the nonlocal delay terms in one and two dimensions are derived in detail,and the bivariate model is transformed into a three-variable reaction-diffusion equation,the conditions of producing steady pattern are obtained.The succession of vegetation pattern over time is obtained by numerical simulation.The results shows that the average vegetation density is positively correlated with the cross diffusion coefficient,that is,with the increase of the cross diffusion coefficient,the average vegetation density will increase.The results of numerical simulation show the effect of cross diffusion coefficient on vegetation pattern.

关 键 词：非局部时滞 交叉扩散 植被 斑图 

分 类 号：Q948[生物学—植物学] O175[理学—数学]