Voir la notice de l'article provenant de la source Math-Net.Ru
@article{MBB_2016_11_2_a11, author = {A. I. Abakumov and Yu. G. Izrailsky}, title = {The harvesting effect on a fish population}, journal = {Matemati\v{c}eska\^a biologi\^a i bioinformatika}, pages = {191--204}, publisher = {mathdoc}, volume = {11}, number = {2}, year = {2016}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/MBB_2016_11_2_a11/} }
A. I. Abakumov; Yu. G. Izrailsky. The harvesting effect on a fish population. Matematičeskaâ biologiâ i bioinformatika, Tome 11 (2016) no. 2, pp. 191-204. http://geodesic.mathdoc.fr/item/MBB_2016_11_2_a11/
[1] Moiseev P. A., Biologicheskie resursy Mirovogo okeana, Agropromizdat, M., 1989
[2] Jørgensen S. E., Lake management. Water development, supply and management, v. 14, Pergamon Press, Oxford, 1980, 167 pp.
[3] Jørgensen S. E., Fath B., A New ecology. Systems perspectives, Elsevier, Amsterdam, 2007, 275 pp.
[4] Poluektov R. A., “Matematicheskie modeli v teorii biologicheskikh populyatsii i soobschestv (istoki stanovleniya i pervye rezultaty)”, Matematicheskaya biologiya i bioinformatika, 7:1 (2012), 4–8 | DOI
[5] Clark C. W., Mathematical bioeconomics. The Mathematics of conservation, Third edition, J. Wiley and Sons Publ., New Jersey, 2010 | MR
[6] Svirezhev Yu. M., Elizarov E. Ya., Problemy kosmicheskoi biologii, v. 20, Matematicheskoe modelirovanie biologicheskikh sistem, Nauka, M., 1972, 160 pp.
[7] Svirezhev Yu. M., Abakumov A. I., Timofeev N. N., “Nekotorye zadachi ekodinamiki ekspluatiruemykh populyatsii i soobschestv”, Problemy ekologicheskogo monitoringa i modelirovaniya ekosistem, 8 (1985), 246–257
[8] Anita S., Analysis and control of age-dependent population dynamics, Kluwer Academic Publishers, Dordrecht, 2000, 200 pp. | MR | Zbl
[9] Ainseba B., Anita S., Langlais M., “Optimal control for a nonlinear age-structured population dynamics model”, Electronic Journal of Differential Equations, 2002:28 (2002), 1–9 (data obrascheniya: 31.08.2016) http://ejde.math.unt.edu
[10] Abakumov A. I., Upravlenie i optimizatsiya v modelyakh ekspluatiruemykh populyatsii, Dalnauka, Vladivostok, 1993, 129 pp.
[11] Leslie P. H., “On the use of matrices in certain population mathematics”, Biometrika, 33:3 (1945), 184–212 | DOI | MR
[12] Neverova G. P., Abakumov A. I., Frisman E. Ya., “Vliyanie promyslovogo iz'yatiya na rezhimy dinamiki limitirovannoi populyatsii: rezultaty modelirovaniya i chislennogo issledovaniya”, Matematicheskaya biologiya i bioinformatika, 11:1 (2016), 1–13 | DOI
[13] Iannelli M., Martcheva M., Milner F. A., Gender-structured population modeling: mathematical methods, numerics and simulations, SIAM, Philadelphia, 2005 | MR | Zbl
[14] Frisman E. Ya., Zhdanova O. L., Kolbina E. A., “Effect of harvesting on the genetic diversity and dynamic behavior of a limited mendelian population”, Russian Journal of Genetics, 46:2 (2010), 239–248 | DOI
[15] Gurtin M. E., Murphy L. F., “On the optimal harvesting of persistent age-structured populations”, J. Math. Biol., 13 (1981), 131–148 | DOI | MR | Zbl
[16] Brokate M., “Pontryagin's principle for control problems in age-dependent population dynamics”, J. Math. Biol., 23 (1985), 75–101 | DOI | MR | Zbl
[17] Gurtin M. E., MacCamy R. C., “Nonlinear age-dependent population dynamics”, Arch. Ration. Mech. Anal., 54 (1974), 281–300 | DOI | MR | Zbl
[18] Iannelli M., Mathematical theory of age-structured population dynamics, Appl. Math. Monographs C. N. R., Giardini Editori e Stampatori, Pisa, 1995
[19] Gurtin M. E., Murphy L. F., “On the optimal harvesting of persistent age-structured populations”, J. Math. Biol., 13 (1981), 131–148 | DOI | MR | Zbl
[20] Murphy L. F., Smith S. J., “Optimal harvesting of an age-structured population”, J. Math. Biol., 29 (1990), 77–90 | DOI | MR | Zbl
[21] Kato N., “Optimal harvesting for nonlinear size-structured population dynamics”, J. Math. Anal. Appl., 342 (2008), 1388–1398 | DOI | MR | Zbl
[22] Abia L. M., Angulo O., López-Marcos J. C., López-Marcos M. A., “Numerical schemes for a size-structured cell population model with equal fission”, Math. Comput. Modelling, 50 (2009), 653–664 | DOI | MR | Zbl
[23] Kato N., “Linear size-structured population models and optimal harvesting problems”, Int. J. Ecol. Dev., F06:5 (2006), 6–19
[24] Anita S., Iannelli M., Kim M. Y., Park E. J., “Optimal harvesting for periodic age-dependent population dynamics”, SIAM J. Appl. Math., 58 (1998), 1648–1666 | DOI | MR | Zbl
[25] Michael G. N., “Marine reserves and optimal harvesting”, Ecology Letters, 6 (2003), 843–849 | DOI
[26] Ricker W. E., Computation and interpretation of biological statistics of fish populations, Bulletin of the Fisheries Research Board of Canada, 191, 1975, 382 pp.
[27] Hilborn R., Fulton E. A., Green B. S., Hartmann K., Tracey S. R., Watson R. A., When is a fishery sustainable?, Canadian Journal of Fisheries and Aquatic Sciences, 72:9 (2015), 1433–1441 | DOI
[28] Anita S., Analysis and control of age-dependent population dynamics, Kluwer Academic Publishers, Dordrecht, 2000 | MR | Zbl
[29] Cantrell R. S., Cosner C., Spatial ecology via reaction-diffusion equations, J. Wiley and Sons Ltd, New York, 2003 | MR | Zbl
[30] Hoar W. S., Randall D. J., Brett J. R. (eds.), Fish physiology, v. 8, Bioenergetics and growth, New York–San Francisco–London, 1979, 407 pp.
[31] Hilborn R., Walters C. J., Quantitative fisheries stock assessment. Choice, dynamics and uncertainty, Chapman and Hall, New York–London, 1992
[32] Abakumov A. I., “Optimalnoe upravlenie populyatsiei s raspredelennymi parametrami”, Informatika i sistemy upravleniya, 2011, no. 29, 3–9
[33] Alekseev V. M., Tikhomirov V. M., Fomin S. V., Optimalnoe upravlenie, Nauka, M., 1979
[34] Fursikov A. V., Optimalnoe upravlenie raspredelennymi sistemami. Teoriya i prilozheniya, Nauchnaya kniga, Novosibirsk, 1999
[35] Cohen D. M., Inada T., Iwamoto T., Scialabba N., FAO species catalogue, An annotated and illustrated catalogue of cods, hakes, grenadiers and other gadiform fishes known to date, v. 10, FAO Fish. Synop., 125, Gadiform fishes of the World (Order Gadiformes) \, no. 10, FAO, Rome, 1990, 442 pp.
[36] Svirezhev Yu. M., Nelineinye volny, dissipativnye struktury i katastrofy v ekologii, Nauka, M., 1987, 368 pp. | MR
[37] Svirezhev Yu. M., Logofet D. O., Ustoichivost biologicheskix soobschestv, Nauka, M., 1978, 352 pp.
[38] Charles A., Garcia S. M., Rice J., “Balanced harvesting in fisheries: economic considerations”, ICES J. Mar. Sci., 2015 (First published online September 10) | DOI