Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (3): 867-880.
Previous Articles Next Articles
Zerong He(),Yimeng Dou,Mengjie Han
Received:
2021-04-16
Online:
2022-06-26
Published:
2022-05-09
Supported by:
CLC Number:
Zerong He,Yimeng Dou,Mengjie Han. Optimal Boundary Control for a Hierarchical Size-Structured Population Model with Delay[J].Acta mathematica scientia,Series A, 2022, 42(3): 867-880.
Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks
1 |
Dewsbury D A . Dominance rank, copulatory behavior, and differential reproduction. The Quarterly Review of Biology, 1982, 57 (2): 135- 159
doi: 10.1086/412672 |
2 |
Henson S M , Cushing J M . Hierarchical models of intra-specific competition: scramble versus contest. J Math Biol, 1996, 34 (7): 755- 772
doi: 10.1007/BF00161518 |
3 |
Jang R J , Cushing J M . A discrete hierarchical model of intra-specific competition. J Math Anal Appl, 2003, 280 (1): 102- 122
doi: 10.1016/S0022-247X(03)00050-7 |
4 |
Gurney W S C , Nisbet R M . Ecological stability and social hierarchy. Theoretical Population Biology, 1979, 16, 48- 80
doi: 10.1016/0040-5809(79)90006-6 |
5 |
Cushing J M . A size-structured model for cannibalism. Theoretical Population Biology, 1992, 42, 347- 361
doi: 10.1016/0040-5809(92)90020-T |
6 |
Cushing J M . The dynamics of hierarchical age-structured populations. J Math Biol, 1994, 32, 705- 729
doi: 10.1007/BF00163023 |
7 | Cushing J M , Li J . Oscilations caused by cannibalism in a size-structured population model. Canadian Applied Mathematics Quarterly, 1995, 3 (2): 155- 172 |
8 |
Calsina Á , Salda$\ddot{\rm n}$a J . Asymptotic behavior of a model of hierarchically structured population dynamics. J Math Biol, 1997, 35, 967- 987
doi: 10.1007/s002850050085 |
9 |
Kraev E A . Existence and uniqueness for height structured hierarchical population models. Natural Resources Modeling, 2001, 14 (1): 45- 70
doi: 10.1111/j.1939-7445.2001.tb00050.x |
10 | Ackleh A S , Deng K . Monotone approximation for a hierarchical age-structured population model. Dynamics of Continuous, Discrete and Impulsive Systems, 2005, 12, 203- 214 |
11 |
Ackleh A S , Deng K , Thibodeaux J J . A monotone approximation for a size-structured population model with a generalized environment. Journal of Biological Dynamics, 2007, 1 (4): 305- 319
doi: 10.1080/17513750701605564 |
12 |
Ackleh A S , Deng K , Hu S . A quasilinear hierarchical size-structured model: well-posedness and application. Appl Math Optim, 2005, 51, 35- 59
doi: 10.1007/s00245-004-0806-2 |
13 |
Shen J , Shu C W , Zhang M . A high order WENO scheme for a hierarchical size-structured population model. J Sci Comput, 2007, 33, 279- 291
doi: 10.1007/s10915-007-9152-x |
14 |
Farkas J Z , Hinow P . Steady states in hierarchical structured populations with distributed states at birth. Discrete and Continuous Dynamical Systems, 2012, 17 (8): 2671- 2689
doi: 10.3934/dcdsb.2012.17.2671 |
15 | Liu Y , He Z . On the well-posedness of a nonlinear hierachical size-structured population model. The ANZIAM Journal, 2017, 58 (3/4): 482- 490 |
16 |
He Z , Ni D , Liu Y . Theory and approximation of solutions to a harvested hierarchical age-structured population model. Journal of Applied Analysis and Computation, 2018, 8 (5): 1326- 1341
doi: 10.11948/2018.1326 |
17 |
何泽荣, 张智强, 裘哲勇. 一类非线性年龄等级结构种群模型的数值解法. 数学物理学报, 2020, 40A (2): 515- 526
doi: 10.3969/j.issn.1003-3998.2020.02.022 |
He Z , Zhang Z , Qiu Z . Numerical method of a nonlinear hierarchical age-structured population model. Acta Mathematica Scientia, 2020, 40A (2): 515- 526
doi: 10.3969/j.issn.1003-3998.2020.02.022 |
|
18 |
何泽荣, 倪冬冬, 王淑平. 一类等级结构种群系统的调控问题. 系统科学与数学, 2018, 38 (10): 1140- 1148
doi: 10.12341/jssms13462 |
He Z , Ni D , Wang S . Control problem for a class of hierarchical population system. Journal of Systems Science and Mathematical Sciences, 2018, 38 (10): 1140- 1148
doi: 10.12341/jssms13462 |
|
19 |
He Z , Ni D , Wang S . Optimal harvesting of a hierarchical age-structured population system. International Journal of Biomathematics, 2019, 12 (8): 1950091
doi: 10.1142/S1793524519500918 |
20 | He Z , Zhou N . Controllability and stabilization of a nonlinear hierarchical age-structured competing system. Electronic Journal of Differential Equations, 2020, 2020 (58): 1- 16 |
21 | Barbu V . Mathematical Methods in Optimization of Differential Systems. Boston: Kluwer Academic Publishers, 1994 |
22 | McDonald J N , Weiss N A . A Course in Real Analysis. Singapore: Elsevier, 2004 |
23 |
Barbu V , Iannelli M . Optimal control of population dynamics. J Optim Theo Appl, 102, 1- 14
doi: 10.1023/A:1021865709529 |
24 | Aniţa S . Analysis and Control of Age-Dependent Population Dynamics. Dordrecht: Kluwer Academic Publishers, 2000 |
[1] | Ying Liu,Jianfang Gao. Oscillation Analysis of a Kind of Systems with Piecewise Continuous Arguments [J]. Acta mathematica scientia,Series A, 2022, 42(3): 826-838. |
[2] | Tailei Zhang,Junli Liu,Mengjie Han. Dynamics of an Anthrax Epidemiological Model with Time Delay and Seasonality [J]. Acta mathematica scientia,Series A, 2022, 42(3): 851-866. |
[3] | Hongmei Cheng,Rong Yuan. Forced Waves of a Delayed Reaction-Diffusion Equation with Nonlocal Diffusion Under Shifting Environment [J]. Acta mathematica scientia,Series A, 2022, 42(2): 491-501. |
[4] | Daoxiang Zhang,Ben Li,Dandan Chen,Yating Lin,Xinmei Wang. Hopf Bifurcation for a Fractional Differential-Algebraic Predator-Prey System with Time Delay and Economic Profit [J]. Acta mathematica scientia,Series A, 2022, 42(2): 570-582. |
[5] | Zerong He,Nan Zhou. Optimal Harvesting in a Competing System of Hierarchical Age-Structured Populations [J]. Acta mathematica scientia,Series A, 2022, 42(1): 228-244. |
[6] | Kaixuan Zhu,Yongqin Xie,Xinyu Mei,Xijun Deng. Uniform Attractors for the Sup-Cubic Weakly Damped Wave Equations with Delays [J]. Acta mathematica scientia,Series A, 2022, 42(1): 86-102. |
[7] | Changyou Wang,Nan Li,Tao Jiang,Qiang Yang. On a Nonlinear Non-Autonomous Ratio-Dependent Food Chain Model with Delays and Feedback Controls [J]. Acta mathematica scientia,Series A, 2022, 42(1): 245-268. |
[8] | Zaiyun Zhang,Zhenhai Liu,Youjun Deng. Global Existence and General Decay for a Nonlinear Viscoelastic Equation with Time-Varying Delay and Velocity-Dependent Material Density [J]. Acta mathematica scientia,Series A, 2021, 41(6): 1684-1704. |
[9] | Zhiyu Zhang,Cheng Zhao,Yuyu Li. Oscillation of Second Order Delay Dynamic Equations with Superlinear Neutral Terms on Time Scales [J]. Acta mathematica scientia,Series A, 2021, 41(6): 1838-1852. |
[10] | Yue Sun,Daoxiang Zhang,Wen Zhou. The Influence of Fear Effect on Stability Interval of Reaction-Diffusion Predator-Prey System with Time Delay [J]. Acta mathematica scientia,Series A, 2021, 41(6): 1980-1992. |
[11] | Guijiang Qin,Jiashan Yang. Oscillation Theorems of Second-Order Variable Delay Dynamic Equations with Quasilinear Neutral Term [J]. Acta mathematica scientia,Series A, 2021, 41(5): 1492-1503. |
[12] | Zerong He,Mengjie Han. Optimal Control of Initial Distributions in a Hierarchical Size-Structured Population System with Delay [J]. Acta mathematica scientia,Series A, 2021, 41(4): 1181-1191. |
[13] | Jingnan Wang,Dezhong Yang. Stability and Bifurcation of a Pathogen-Immune Model with Delay and Diffusion Effects [J]. Acta mathematica scientia,Series A, 2021, 41(4): 1204-1217. |
[14] | Zhiyu Zhang. Oscillation Criteria of Second-Order Generalized Emden-Fowler Delay Differential Equations with a Sub-Linear Neutral Term [J]. Acta mathematica scientia,Series A, 2021, 41(3): 811-826. |
[15] | Xiling Li,Fei Gao,Wenqin Li. Stability Analysis of Fractional-Order Hepatitis B Virus Infection Model With Immune Delay [J]. Acta mathematica scientia,Series A, 2021, 41(2): 562-576. |
|