Geodesic
On a~one control game problem for the age-structured population
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 3 (2011) no. 3, pp. 3-16.

Voir la notice de l'article provenant de la source Math-Net.Ru

The game problem of management of age-structured population is considered. The age-dependent population dynamics is described using McKendrick–von Voerster model. There is a set of independent players, each of them has own criterion of utility. The example of numeric solution of the problem is considered.
Keywords: optimal harvesting, age-structured population dynamics. 
@article{MGTA_2011_3_3_a0,
     author = {Oleg I. Il'in},
     title = {On a~one control game problem for the age-structured population},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {3--16},
     publisher = {mathdoc},
     volume = {3},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2011_3_3_a0/}
}
TY  - JOUR
AU  - Oleg I. Il'in
TI  - On a~one control game problem for the age-structured population
JO  - Matematičeskaâ teoriâ igr i eë priloženiâ
PY  - 2011
SP  - 3
EP  - 16
VL  - 3
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MGTA_2011_3_3_a0/
LA  - ru
ID  - MGTA_2011_3_3_a0
ER  - 
%0 Journal Article
%A Oleg I. Il'in
%T On a~one control game problem for the age-structured population
%J Matematičeskaâ teoriâ igr i eë priloženiâ
%D 2011
%P 3-16
%V 3
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MGTA_2011_3_3_a0/
%G ru
%F MGTA_2011_3_3_a0
Oleg I. Il'in. On a~one control game problem for the age-structured population. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 3 (2011) no. 3, pp. 3-16. http://geodesic.mathdoc.fr/item/MGTA_2011_3_3_a0/

[1] Abakumov A. I., Upravlenie i optimizatsiya v modelyakh ekspluatiruemykh populyatsii, Dalnauka, Vladivostok, 1993, 129 pp.

[2] Biverton R., Kholt S., Dinamika chislennosti promyslovykh ryb, Pischevaya promyshlennost, M., 1969, 248 pp.

[3] R. A. Poluektov (red.), Dinamicheskaya teoriya biologicheskikh populyatsii, Nauka, M., 1974, 456 pp.

[4] Zakharov V. V., Petrosyan A. A., “Teoretiko-igrovoi podkhod k probleme okruzhayuschei sredy”, Vestnik Leningr. un-ta, 1981, no. 1, Ser. matem., mekh., astronom., No 1, 26–32 | Zbl

[5] Ilin O. I., “Ob optimalnoi ekspluatatsii populyatsii ryb s vozrastnoi strukturoi”, Sibirskii zhurnal industrialnoi matematiki, 10:3(31) (2007), 43–57 | MR | Zbl

[6] Ilin O. I., Zadachi optimizatsii v nepreryvnykh modelyakh ekspluatiruemykh populyatsii s vozrastnoi strukturoi, Avtoref. diss. $\dots$ kand. fiz.-mat. nauk, KamchatNIRO, Petropavlovsk-Kamchatskii, 2009, 22 pp.

[7] Mazalov V. V., Rettieva A. N., “Ob odnoi zadache upravleniya bioresursami”, Obozrenie prikladnoi i promyshlennoi matematiki, 9:2 (2002), 293–306

[8] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mischenko E. F., Matematicheskaya teoriya optimalnykh protsessov, Gos. izd-vo fiz.-mat. lit., M., 1961, 391 pp. | MR | Zbl

[9] Rettieva A. N., Metody dinamicheskikh igr v zadache upravleniya bioresursami: podkhod s vvedeniem zapovednoi zony, Avtoref. diss. $\dots$ kand. fiz.-mat. nauk, IPMI KarNTs RAN, Petrozavodsk, 2004, 23 pp.

[10] Rikker U. E., Metody otsenki i interpretatsiya biologicheskikh pokazatelei populyatsii ryb, Pischevaya promyshlennost, M., 1979, 408 pp.

[11] Banks H. T., Kappel F., Wang C., “Weak solutions and differentiability for size-structured population models”, Estimation and control of distributed parameter systems, Int. Ser. Numer. Math., 100, 1991, 35–50 | MR | Zbl

[12] Chan W. L., Guo Bao Zhu, “Overtaking optimal control problem of age-dependent populations with infinite horizon”, J. of Mathematical Analysis and Applications, 150 (1990), 41–53 | DOI | MR | Zbl

[13] Feichtinger G., Tragler G., Veliov V. M., “Optimality conditions for age-structured control systems”, J. of Mathematical Analysis and Applications, 288 (2003), 47–68 | DOI | MR | Zbl

[14] von Foerster H., “Some remarks on changing populations”, The Kinetics of cellular proliferation, N.Y., 1959, 382–407

[15] Hilborn R., Walters C. J., Quantitative Fisheries Stock Assessment: Choice, Dynamics and Uncertainty, Chapman and Hall, N.Y., 1992, 570 pp.

[16] Sinko J. W., Streifer W., “A new model for age-sized structure for population”, Ecology, 48 (1967), 910–918 | DOI