Creation of locally disconnected basin boundary of attractors in population dynamics model
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2012), pp. 59-69 Cet article a éte moissonné depuis la source Math-Net.Ru

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Nonlinear dynamic system used for simulation of fish population with application of computing tools is analyzed. Such phenomena as rout to chaos by way of period doubling cascade, intermittency, subduction, interior crisis of strange attractor are considered. New stock-recruitment models are developed which have ability to move one of two existing attractors. Basin boundaries of a hybrid-time model becomes fractal-like which is reduced to chaotic transient behavior.
Keywords: basin boundaries of attractors, modeling of population dynamics.
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A. Yu. Perevarukha. Creation of locally disconnected basin boundary of attractors in population dynamics model. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2012), pp. 59-69. http://geodesic.mathdoc.fr/item/VSPUI_2012_3_a5/

[1] Li T., Yorke J., “Period three implies chaos”, Amer. Math. Monthly, 82:10 (1975), 985–990 | DOI | MR

[2] Henon M., “2-Dimensional mapping with a strange attractor”, Comm. Math. Phys., 50 (1976), 69–77 | DOI | MR

[3] Magnitskii N. A., Oginova Yu. V., “Issledovanie stsenariya perekhoda k khaosu v modeli ekologicheskoi sistemy”, Trudy In-ta sistemnogo analiza RAN, 14 (2005), 190–197

[4] Frisman E. Ya., Skaletskaya E. I., “Strannye attraktory v prosteishikh modelyakh dinamiki chislennosti biologicheskikh populyatsii”, Obozrenie prikladnoi i promyshlennoi matematiki, 1:6 (1994), 988–1004

[5] Ott E., Chaos in dynamical systems, Cambridge University Press, Cambridge, 1993, 386 pp. | MR

[6] Ricker W., “Stock and recruitment”, J. of the Fisheries research board of Canada, 11:5 (1954), 559–623 | DOI

[7] Milnor J, “On the concept of attractor”, Commun. Math. Phys., 99 (1985), 177–195 | DOI | MR | Zbl

[8] Malinetskii G. G., Potapov A. B., Nelineinaya dinamika i khaos, KomKniga, M., 2006, 240 pp.

[9] Alligood K., Yorke E., Yorke J., “Why period-doubling cascades occur: periodic orbit creation followed by stability shedding”, Physica D, 28 (1987), 181–200 | DOI | MR

[10] Feigenbaum M. J., “Universal behavior in nonlinear systems”, Physica D, 7:1–3 (1983), 16–39 | DOI | MR

[11] Arnold V. I., Afraimovich V. S., Ilyashenko Yu. S., Shilnikov L. P., “Teoriya bifurkatsii”, Sovremennye problemy matematiki. Fundamentalnye napravleniya, 5, 1985, 5–220

[12] Witt A., Feudel U., Pikovsky A., “Birth of strange nonchaotic attractors due to interior crisis”, Physica D, 109 (1997), 180–190 | DOI | MR | Zbl

[13] Zhivotovskii L. A., Khramtsov V. V., “Model dinamiki chislennosti gorbushi Oncorhynchus gorbusha”, Voprosy ikhtiologii, 36:3 (1996), 369–385

[14] Farmer J., Ott E., Yorke J., “The dimension of chaotic attractors”, Physica D, 7 (1983), 153–170 | DOI | MR

[15] Grebogi C., Ott E., Yorke J. A., “Crises, sudden changes in chaotic attractors and transient chaos”, Physica D, 7 (1983), 181–200 | DOI | MR

[16] Grebogi C., Ott E., Yorke J. A., “Fractal basin boundaries, long-lived chaotic transients and unstable-unstable pair bifurcation”, Phys. Rev. Letters, 50:13 (1983), 935–938 | DOI | MR

[17] Jeffries C., Perez J., “Direct observation of crises of the chaotic attractor in a nonlinear oscillator”, Phys. Rev. A, 27:1 (1983), 601–603 | DOI | MR

[18] Perevaryukha A. Yu., “Gibridnye modeli dinamiki bioresursov: ravnovesie, tsikl i perekhodnyi khaos”, Avtomatika i vychislitelnaya tekhnika, 2011, no. 4, 55–68

[19] Sharkovskii A. N., Kolyada S. F., Sivek A. G., Fedorenko V. V., Dinamika odnomernykh otobrazhenii, Naukova dumka, Kiev, 1989, 216 pp.

[20] Magnitskii N. A., Sidorov S. V., Novye metody khaoticheskoi dinamiki, Editorial URSS, M., 2004, 320 pp.

[21] Peterman R. M., “A simple mechanism that causes collapsing stability regions in exploited salmonid population”, J. of the Fisheries research board of Canada, 34 (1977), 1130–1142 | DOI

[22] Vasnetsov V. V., “Etapy razvitiya kostistykh ryb”, Ocherki po obschim voprosam ikhtiologii, ed. E. N. Pavlovskii, Izd-vo AN SSSR, M., 1953, 207–217

[23] Kolesov Yu. B., Senichenkov Yu.B., Modelirovanie sistem. Dinamicheskie i gibridnye sistemy, BKhV, SPb., 2006, 224 pp.

[24] Teoriya sistem s peremennoi strukturoi, ed. E. S. Emelyanov, Nauka, M., 1970, 590 pp.

[25] Perevaryukha A. Yu., “Nelineinye effekty i perekhodnye rezhimy v dinamike novykh modelei upravleniya bioresursami”, Trudy SPIIRAN, 16, 2011, 243–255 | Zbl

[26] Senichenkov Yu. B., Chislennoe modelirovanie gibridnykh sistem, Izd-vo Politekhn. un-ta, SPb., 2004, 206 pp.

[27] MacDonald S., Grebogi C., Ott E., Yorke J., “Fractal basin boundaries”, Physica D, 17:2 (1985), 125–153 | DOI | MR

[28] Grebogi C., Ott E., Yorke J, “Metamorphoses of basin boundaries in nonlinear dynamical system”, Phys. Rev. Letters, 56:10 (1986), 1011–1016 | DOI | MR

[29] Hirsch E., Huberman B., Scalapino J., “Theory of intermittency”, Phys. Rev. A, 25:1 (1982), 519–532 | DOI

[30] Silchenko A., Beri S., Luchinsky D., “Fluctuation transition across different kinds of fractal basin boundaries”, Phys. Rev. E, 71 (2005), 203–211 | DOI | MR

[31] Nusse H. E., Yorke J. A., “Basins of attraction, Wada basin boundaries and basin cells”, Science, 271 (1996), 1376–1380 | DOI | MR | Zbl

[32] Perevaryukha Yu. N., Geraskin P. P., Perevaryukha T. Yu., “Sravnitelnyi immunokhimicheskii analiz vnutrividovykh osobennostei syvorotochnykh belkov sevryugi Acipenser stellatus Kaspiiskogo basseina”, Voprosy ikhtiologii, 51:3 (2011), 405–410

[33] Geraskin P. P., Metallov G. F., Perevaryukha Yu. N., “Fiziologicheskie i populyatsionno-geneticheskie issledovaniya kaspiiskikh ryb”, Rybnoe khozyaistvo, 2007, no. 3, 66–68 | MR