带分布时滞的具有尺度结构的种群模型的异步指数增长
Asynchronous Exponential Growth for a Size-structured Two-phase Population Model with Delayed Birth Process
摘要
研究一个带分布时滞的具有尺度结构的种群模型.模型将个体分为"活跃"期和"休眠"期两个阶段研究.利用算子半群的理论证明了此模型的适定性并证明此模型的解具有异步指数增长的状态.
In this paper we study a size-structured two-phase population model with delayed birth process. We establish the well-posedness for this model and show that the solution of this model has asynchronous exponential growth by means of semigroups.
出处
《数学的实践与认识》
CSCD
北大核心
2014年第12期170-178,共9页
Mathematics in Practice and Theory
基金
国家自然科学基金(11171295
11226182
11301474))
广东省高等学校优秀青年教师培养计划(Yq2013163)
肇庆市科技创新计划项目
肇庆学院自然科学基金资助
关键词
尺度结构
分布时滞
适定性
异步指数增长
算子半群
Size-structured populations
distributed delay
well-posedness
asynchronousexponential growth
semigroups.
参考文献11
-
1Farkas J Z, and Hinow P. On a size-structured two-phase population model with infinite states-at- birth[J]. Positivity, 2010, 14(3): 501-514.
-
2Farkas J Z, Green D W, and Hinow P. Semigroup analysis of structured parasite populations[J]. Mathematical Modelling of Natural Phenomena, 2010(5): 94-114.
-
3Auslander D M, Oster G F, and Huffaker C B. Dynamics of interacting populations[J]. J. Franklin Inst, 1974(297): 345-376.
-
4Piazzera S, and Tonetto L. Asynchronous exponential growth for an age dependent population equation with delayed birth process[J]. J Evol Equ, 2005(5): 61-77.
-
5Batkai A, and Piazzera S. Semigroups and linear partial differential equations with delay[J]. J Math Anal Appl, 2001(264): 1-20.
-
6王定江.非线性年龄依赖细胞分裂模型[J].数学的实践与认识,2007,37(8):7-12. 被引量：2
-
7Dyson J, Villella-Bressan R, Webb G F. Asynchronous exponential growth in an age population of proliferating and quienscent cells[J]. Math Biosci, 2002, 177-178: 73-83.
-
8Thieme H R. Balanced exponential growth of operator semigroups[J]. J Math Anal Appl 30-49. structured 1998(223).
-
9Engel K J, and Nagel R. One-parameter Semigroups for Linear Evolution Equations[M]. Springer New York, 2000.
-
10Ph. Clement H, Heijmans S, Angenent C, van Duijin and B. de Pagter. One-Parameter Semigroups[M]. North-holland, Amsterdam, 1987.
二级参考文献8
-
1[1]Dyson J,Villella-Bressan R,Webb G F.A nonliear age and maturity structureed model of population dynamics.Ⅰ.Basic Theory[J].J Math Anal Appl,2000,242:93-104.
-
2[2]Dyson J,Villella-Bressan R,Webb G F.A nonliear age and maturity structureed model of population dynamics.Ⅱ.Chaos[J].J Math Anal Appl,2000,242:255-270.
-
3[3]Webb G F.Theory of Nonliear Age-Dependent Population Dynamics[M].Marcel Dekker,New York,1985.
-
4[4]Hisashi Inaba.Nonliear dynamics of open marine population with space-limited recruitment:The case of mortality control[J].J Math Anal Appl,2002,275:537-556.
-
5[5]Nobuyuki Kato,Kazushige Sato.Continuous dependence results for a general model of size-dependent population dynamics[J].J Math Anal Appl,2002,272:200-222.
-
6[6]Mostafa ADIMY.Laurent PUJO-MENJOUET.Asymptotic behavior of a singular transport equation modelling cell division[J].Cont and Disc Dynam Syst Ser B,2003,3(1):439-456.
-
7[7]Mackey M C,Rudnicki R.Global stability in a delayed partial differential equation describing cellular replication[J].J Math Biol,1994,33:89-109.
-
8[8]Mackey M C,Rudnicki R.A new criterion for the global stability of simultaneous cell replication and maturation processes[J].J Math Biol,1999,38:195-219.
-
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-
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-
3徐若翰.行程问题与分段函数[J].数学大世界（初中版）,2010(7):9-9.
-
4厚宇德.实验物理学家如何更早取得重要成果[J].物理实验,2016,36(8):21-24.
-
5范善康.“收获教学”的教学策略——收获教学第三阶段研究之三[J].福建基础教育研究,2009(11):86-89.
-
6吴肖,王笑君,许泽燕.利用数据采集器探究电磁感应现象[J].物理教师（高中版）,2005,26(5):35-37.
-
7薛社生,刘家骢,彭金华.液体燃料爆炸抛撒的近场阶段研究[J].南京理工大学学报,1997,21(4):333-336. 被引量：9
-
8严防黑恶势力戴“红帽子”寻靠山[J].新农民（下半月）,2010(5):8-8.
-
9西班牙稀产量大幅度增长[J].中国果业信息,2005,22(5X):38-38.
-
10董亚会,李恒.中国优势项目运动员形态特征和训练阶段研究[J].内江科技,2011,32(7):24-24.
