演化区域上的广义Logistic模型的扩散特征  

The Diffusive Characteristics of the Generalized Logistic Model onan Evolving Domain

作　　者：徐海燕 葛静 林支桂[1] XU Haiyan;GE Jing;LIN Zhigui(School of Mathematical Science,Yangzhou University,Yangzhou Jiangshu 225002,China;School of Mathematics and Statistics,Huaiyin Normal University,Huaian Jiangshu 223300,China)

机构地区：[1]扬州大学数学科学学院,江苏扬州225002 [2]淮阴师范学院数学与统计学院,江苏淮安223300

出　　处：《江西师范大学学报（自然科学版）》2020年第4期345-349,共5页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11771381,11701206,11911540464)资助项目.

摘　　要：该文研究广义Logistic反应扩散模型,该模型描述了周期演化区域上的物种扩散.首先由区域的增长为各向同性,将模型转化为固定区域上的反应扩散问题;其次利用特征值问题和上下解方法给出了其正周期解的渐近性态;最后通过对阈值的分析,解释了栖息地区域周期性变化对物种生存产生的影响.The generalized logistic reaction diffusion model,which describes diffusion of species on a periodic evolving domain,is discussed.Firstly,by assuming that the evolving domain is isotropic,the model is transformed into the reaction diffusion problem in a fixed domain.Secondly,the asymptotic behavior of positive periodic solutions is presented by utilizing eigenvalue problem as well as upper and lower solution methods.Lastly,through the analysis of the threshold,the impacts of regional evolution on survival of species are expressed.

关 键 词：扩散模型 广义Logistic方程 周期演化 渐近性态 

分 类 号：O175.26[理学—数学]