干旱半干旱地区变时滞反应扩散植被-水系统的阈值动力学  

Threshold Dynamics of a Reaction-Diffusion Vegetation-Water Systems with Time Delay in Arid Area and Semi-arid Regions

作　　者：胡静 朱磊[1] 任杰 吴涵 张启敏 HU Jing;ZHU Lei;REN Jie;WU Han;ZHANG Qimin(School of Civil Engineering and Water Conservancy,Ningxia University,Yinchuan 750021,China;School of Mathematics and Statistics,Ningxia University,Yinchuan 750021,China;School of Medical Information and Engineering,Ningxia Medical University,Yinchuan 750021,China;Ningxia Basic Science Research Center of Mathematics,Ningxia University,Yinchuan 750021,China;Coca-Cola Beverages(Shanghai)Company Limited,Shanghai 200123,China)

机构地区：[1]宁夏大学土木与水利工程学院,宁夏银川750021 [2]宁夏大学数学统计学院,宁夏银川750021 [3]宁夏医科大学医学信息与工程学院,宁夏银川750021 [4]宁夏数学基础学科研究中心,宁夏银川750021 [5]可口可乐(饮料)上海有限公司,上海200123

出　　处：《应用数学》2025年第1期71-78,共8页Mathematica Applicata

基　　金：国家自然科学基金(12301630,12161068,12201331);宁夏自然科学基金(2023AAC03085,2023AAC03181);宁夏回族自治区全职引进高层次人才科研启动项目(2023BSB03070,2022BSB03083)。

摘　　要：考虑地表水的渗透和扩散作用对干旱半干旱地区生态系统的影响,本文建立了具有时变时滞的反应扩散植被-水系统模型.给出阈值R^(*),并讨论了系统的动力学行为,当R^(*)<1时,系统的无植被平衡点局部渐近稳定.当R^(*)>1,植被一致持久.此外,通过拉丁方抽样(LHS)及偏秩相关系数(PRCCs)方法对模型阈值进行敏感性分析,给出了参数对系统动力学行为的影响并为制定防治荒漠化的措施提出建议.此外,通过分析系统有限时间稳定性,讨论了时滞对植被水模型的动力学行为的影响.Considering the effects of infiltration and diffusion of surface water on the ecosystems in arid and semi-arid areas,a reaction-diffusion vegetation-water system with time-varying delay is established in this paper.A threshold value R^(*)is defined,and the dynamic behaviors of the system related to the threshold value are discussed.When R^(*)>1,the vegetation-free equilibrium point of the system is locally asymptotically stable.When R^(*)<1,the vegetation is uniformly persistent.In addition,the sensitivity analysis of the threshold is carried out by Latin Hypercube Sampling(LHS)and partial rank correlation coefficients(PRCCs)methods,the influence of parameters on the dynamic behaviors of the system is discussed,and some suggestions for measures to prevent desertification are given.In addition,the influence of time delay on the dynamic behaviors of the vegetation-water system are discussed,by analyzing the finite-time stability of the system.

关 键 词：植被-水模型 阈值动力学 反应扩散 敏感性分析 有限时间稳定 

分 类 号：O175.14[理学—数学]