[1]徐海燕,葛 静,林支桂*.演化区域上的广义Logistic模型的扩散特征[J].江西师范大学学报(自然科学版),2020,(04):345-349.[doi:10.16357/j.cnki.issn1000-5862.2020.04.04]
　XU Haiyan,GE Jing,LIN Zhigui*.The Diffusive Characteristics of the Generalized Logistic Model on an Evolving Domain[J].Journal of Jiangxi Normal University:Natural Science Edition,2020,(04):345-349.[doi:10.16357/j.cnki.issn1000-5862.2020.04.04]
点击复制

演化区域上的广义Logistic模型的扩散特征()
分享到：

《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2020年04期
页码:
345-349
栏目:
数学与应用数学
出版日期:
2020-08-10

文章信息/Info

Title:
The Diffusive Characteristics of the Generalized Logistic Model on an Evolving Domain
文章编号:
1000-5862(2020)04-0345-05
作者:
徐海燕1; 葛 静2; 林支桂1*
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
Author(s):
XU Haiyan1; GE Jing2; LIN Zhigui1*
1.School of Mathematical Science,Yangzhou University,Yangzhou Jiangshu 225002,China; 2.School of Mathematics and Statistics,Huaiyin Normal University,Huaian Jiangshu 223300,China
关键词:
扩散模型;  广义Logistic方程;  周期演化;  渐近性态
Keywords:
diffusive model;  generalized logistic equation;  periodic evolution;  asymptotic behavior
分类号:
O 175.26
DOI:
10.16357/j.cnki.issn1000-5862.2020.04.04
文献标志码:
A
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.
Abstract:
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.

参考文献/References:

[1] Freedman H I.Deterministic mathematical models in population ecology[M].New York:Marcel Dekker Incorporate,1980.
[2] 杨琪瑜.单种群生长的广义Logistic模型中参数的一种估值方法[J].生物数学学报,1997,12(4):316-320.
[3] 王寿松.单种群生长的广义Logistic模型[J].生物数学学报,1990,7(1):23-27.
[4] Lin Ke,Mu Chunlai,Zhong Hua.A blow-up result for a quasilinear chemotaxis system with logistic source in higher dimensions[J].J Math Anal Appl,2018,464(1):435-455.
[5] Lin Ke,Mu Chunlai.Global dynamics in a fully parabolic chemotaxis system with logistic source[J].Discrete and Continuous Dynamical Systems,2016,36(9):5025-5046.
[6] Viglialoro G.Very weak global solutions to a parabolic-parabolic chemotaxis-system with logistic source[J].J Math Anal Appl,2016,439(1):197-212.
[7] Liu Ling,Zheng Jiashan.Global existence and boundedness of solution of a parabolic-parabolic-ode chemotaxis-haptotaxis model with(generalized)logistic source[J].Discrete and Continuous Dynamical Systems-B,2019,24(7):3357-3377.
[8] Tao Youshan.Global existence of classical solutions to a combined chemotaxis-haptotaxis model with logistic source[J].J Math Anal Appl,2009,354(1):60-69.
[9] Tello J I,Winkler M.A chemotaxis system with logistic source[J].Communications in Partial Differential Equations,2007,32(6):849-877.
[10] Du Yihong,Lin Zhigui.Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary[J].SIAM Journal on Mathematical Analysis,2010,42(1):377-405.
[11] 林支桂.数学生态学导引[M].北京:科学出版社,2013:145-148.
[12] 唐秋林.增长区域上具扩散的Logistic方程解的渐近性[D].扬州:扬州大学,2011.
[13] Jiang Danhua,Wang Zhicheng.The diffusive logistic equation on periodically evolving domains[J].J Math Anal Appl,2018,458(1):93-111.
[14] 孙素梅,孟悦,朱家桢,等.周期演化区域上的Logistic捕获模型的动力学分析[J].生物数学学报,2018(1):84-90.
[15] Hess P.Periodic-parabolic boundary value problems and positivity[M].Halow,UK:Longman Scientific and Technical,1991.
[16] Kato T.Perturbation theory for linear operators[M].New York:Springer-Verlag,1966.

备注/Memo

备注/Memo:
收稿日期:2020-03-12
基金项目:国家自然科学基金(11771381,11701206,11911540464)资助项目.
通信作者:林支桂(1965-),男,江苏兴化人,教授,博士,博士生导师,主要从事生物数学方面的研究.E-mail:zglin@yzu.edu.cn
更新日期/Last Update: 2020-08-10