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Control problems of an age-dependent predator-prey system. (English) Zbl 1212.35485
Summary: This paper is concerned with optimal harvesting problems for a system consisting of two populations with age-structure and interaction of predator-prey. Existence and uniqueness of non-negative solutions to the system and the continuous dependence of solutions on control variables are investigated. Existence of optimal policy is discussed, optimality conditions are derived by means of normal cone and adjoint system techniques.
MSC:
35Q93PDEs in connection with control and optimization
35B50Maximum principles (PDE)
49J20Optimal control problems with PDE (existence)
49K20Optimal control problems with PDE (optimality conditions)
92D40Ecology
References:
[1]Rorres C, Fair W. Optimal age specific harvesting policy for continuous-time population model, In: T A Burton ed, Modelling and Differential Equations in Biology, New York: Marcel Dekker, 1980.
[2]Ainseba B, Langlais M. On a population dynamics control problem with age dependence and spatial structure, J Math Anal Appl, 2000, 248: 455–474. · Zbl 0964.93045 · doi:10.1006/jmaa.2000.6921
[3]Barbu V, Iannelli M, Martcheva M. On the controllability of the Lotka-Mckendrick model of population dynamics, J Math Anal Appl, 2001, 253: 142–165. · Zbl 0961.92024 · doi:10.1006/jmaa.2000.7075
[4]Barbu V, Iannelli M. Optimal control of population dynamics, J Optim Theory Appl, 1999, 102: 1–14. · Zbl 0984.92022 · doi:10.1023/A:1021865709529
[5]Anita S. Analysis and Control of Age-Dependent population Dynamics, Dordrecht: Kluwer Academic Publishers, 2000.
[6]Hritonenko N, Yatsenko Y. Optimization of harvesting age in an integral age-dependent model of population dynamics, Math Biosci, 2005, 195: 154–167. · Zbl 1065.92058 · doi:10.1016/j.mbs.2005.03.001
[7]Hritonenko N, Yatsenko Y. Optimization of harvesting return from age-structured population, J Bioeconomics, 2006, 8: 167–179. · doi:10.1007/s10818-006-9000-3
[8]Brokate M. Pontryagin’s principle for control problems in age-dependent population dynamics, J Math Biol, 1985, 23: 75–101.
[9]Anita S, Iannelli M, Kim M-Y, et al. Optimal harvesting for periodic age-dependent population dynamics, SIAM J Appl Math, 1998, 58: 1648–1666. · Zbl 0935.92030 · doi:10.1137/S0036139996301180
[10]Busoni G, Matucci S. A problem of optimal harvesting policy in two-stage age-dependent populations, Math Biosci, 1997, 143: 1–33. · Zbl 0924.92019 · doi:10.1016/S0025-5564(97)00011-4
[11]Fister K R, Lenhart S. Optimal control of a competitive system with age-structure, J Math Anal Appl, 2004, 291: 526–537. · Zbl 1043.92031 · doi:10.1016/j.jmaa.2003.11.031
[12]He Z R. Optimal birth control of age-dependent competitive species, J Math Anal Appl, 2004, 296: 286–301. · Zbl 1075.92045 · doi:10.1016/j.jmaa.2004.04.052
[13]He Z R. Optimal birth control of age-dependent competitive species. II. Free horizon problems, J Math Anal Appl, 2005, 305: 11–28. · Zbl 1096.92043 · doi:10.1016/j.jmaa.2004.10.002
[14]He Z R. Optimal harvesting of two competing species with age dependence, Nonlinear Anal: Real World Appl, 2006, 7: 769–788. · Zbl 1105.35303 · doi:10.1016/j.nonrwa.2005.04.005
[15]Luo Z, He Z R, Li W T. Optimal birth control for predator-prey system of three species with age-structure, Appl Math Comput, 2004, 155: 665–685. · Zbl 1068.92040 · doi:10.1016/S0096-3003(03)00808-7
[16]Luo Z, He Z R, Li W T. Optimal birth control for an age-dependent n-dimensional food chain model, J Math Anal Appl, 2003, 287: 557–576. · Zbl 1044.92046 · doi:10.1016/S0022-247X(03)00569-9
[17]Luo Z. Optimal harvesting control problem for an age-dependent competing system of n species, Appl Math Comput, 2006, 183: 119–127. · Zbl 1108.92043 · doi:10.1016/j.amc.2006.05.180
[18]Luo Z. Optimal harvesting control problem for an age-dependent n-dimensional food chain diffusion model, Appl Math Comput, 2007, 186: 1742–1752. · Zbl 1111.92061 · doi:10.1016/j.amc.2006.08.168
[19]Zhao C, Wang M, Zhao P. Optimal harvesting problems for age-dependent interacting species with diffusion, Appl Math Comput, 2005, 163: 117–129. · Zbl 1066.92062 · doi:10.1016/j.amc.2004.01.030
[20]Zhao C, Wang M, Zhao P. Optimal control of harvesting for age-dependent predator-prey system, Math Comput Modelling, 2005, 42: 573–584. · Zbl 1088.92063 · doi:10.1016/j.mcm.2004.07.019
[21]Iannelli M. Mathematical Theory of Age-Structured Population Dynamics, Pisa: Giardini Editori E Stampatori, 1995.
[22]Yosida K. Functional Analysis, 6 ed, Berlin: Springer-Verlag, 1980.
[23]Iannelli M, Milner F A. On the approximation of the Lotka-Mckendrick equation with finite life-span, J Comput Appl Math, 2001, 136: 245–254. · Zbl 0998.65103 · doi:10.1016/S0377-0427(00)00616-6