The buffer phenomenon in mathematical models of natural sciences
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2010), pp. 58-63 Cet article a éte moissonné depuis la source Math-Net.Ru

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We say that in mathematical model of nonlinear distributed self-oscillatory system the buffer phenomenon is observed if in this model there is any predetermined finite numbers of attractors of the same type (stable equilibrium states, stable periodic solutions, etc.) for an appropriate choice of its parameters. We investigate some mathematical models of natural sciences, which exhibit the buffer phenomenon.
Keywords: distributed self-oscillatory system, attractor, buffer phenomenon.
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N. Kh. Rozov. The buffer phenomenon in mathematical models of natural sciences. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2010), pp. 58-63. http://geodesic.mathdoc.fr/item/VUU_2010_3_a6/

[1] Vitt A. A., “Raspredelennye avtokolebatelnye sistemy”, Zhurn. tekhn. fiz., 4:1 (1934), 144–157

[2] Vitt A. A., “K teorii skripichnoi struny”, Zhurn. tekhnich. fiz., 6:9 (1936), 1459–1479

[3] Azyan Yu. M., Migulin V. V., “Ob avtokolebaniyakh v sistemakh s zapazdyvayuschei obratnoi svyazyu”, Radiotekhnika i elektronika, 1:4 (1956), 126–130

[4] Zakharov A. A., Kolesov Yu. S., “Prostranstvenno neodnorodnye rezhimy v zadache khischnik-zhertva”, Nelineinye kolebaniya i ekologiya, Yaroslavl, 1984, 3–15 | MR

[5] Kolesov A. Yu., Kolesov Yu. S., “Bifurkatsiya avtokolebanii singulyarno vozmuschennogo volnovogo uravneniya”, DAN SSSR, 315:2 (1990), 281–283 | MR | Zbl

[6] Kolesov A. Yu., Mischenko E. F., Rozov N. Kh., “Asimptoticheskie metody issledovaniya periodicheskikh reshenii nelineinykh giperbolicheskikh uravnenii”, Tr. MIAN, 222, 1998, 1–192 | MR

[7] Kolesov A. Yu., Mischenko E. F., Rozov N. Kh., “Yavlenie bufernosti v rezonansnykh sistemakh nelineinykh giperbolicheskikh uravnenii”, Uspekhi matem. nauk, 55:2 (2000), 95–120 | DOI | MR | Zbl

[8] Kolesov A. Yu., Mischenko E. F., Rozov N. Kh., “Fenomen bufernosti v nelineinoi fizike”, Tr. MIAN, 250, 2005, 112–182 | MR | Zbl

[9] Kolesov A. Yu., Rozov N. Kh., “K voprosu o teoreticheskom ob'yasnenii yavleniya diffuzionnoi bufernosti”, Zhurn. vychislit. matem. i matem. fiz., 44:11 (2004), 2020–2040 | MR | Zbl

[10] Kolesov A. Yu., Rozov N. Kh., “Asimptoticheskaya teoriya kolebanii v sisteme Vitta”, Itogi nauki i tekhniki. Ser. Sovremennaya matematika i ee prilozheniya, 67, VINITI, M., 1999, 5–68 | MR | Zbl

[11] Kolesov A. Yu., Mischenko E. F., Rozov N. Kh., “Yavlenie bufernosti v sistemakh, blizkikh k dvumernym gamiltonovym”, Tr. In-ta matem. i mekh. UrO RAN, 12, no. 1, 2006, 103–141

[12] Kolesov A. Yu., Rozov N. Kh., “O prirode yavleniya bufernosti v slabo dissipativnykh sistemakh”, Teor. i matem. fiz., 146:3 (2006), 447–466 | DOI | MR | Zbl

[13] Kolesov Yu. S., “Asimptotika i ustoichivost nelineinykh parametricheskikh kolebanii singulyarno vozmuschennogo telegrafnogo uravneniya”, Matem. sb., 186:10 (1995), 57–72 | MR | Zbl

[14] Kolesov A. Yu., Rozov N. Kh., “Yavlenie bufernosti v RCLG-avtogeneratore: teoreticheskii analiz i rezultaty eksperimenta”, Tr. MIAN, 233, 2001, 153–207 | MR | Zbl

[15] Kolesov A. Yu., Rozov N. Kh., “Yavlenie bufernosti v raspredelennykh mekhanicheskikh sistemakh”, Prikl. matem. i mekh., 65:2 (2001), 183–198 | MR | Zbl

[16] Kolesov A. Yu., Rozov N. Kh., “Opticheskaya bufernost i mekhanizmy ee vozniknoveniya”, Teor. i matem. fiz., 140:1 (2004), 14–28 | DOI | MR | Zbl

[17] Kolesov A. Yu., Rozov N. Kh., “Yavlenie bufernosti v teorii goreniya”, Dokl. AN, 396:2 (2004), 170–173 | MR | Zbl

[18] Kolesov A. Yu., Rozov N. Kh., “Diffuzionnaya bufernost v odnoi matematicheskoi modeli biologii”, Izv. RAN. Ser. Matem., 62:5 (1998), 135–164 | DOI | MR | Zbl

[19] Mischenko E. F., Sadovnichii V. A., Kolesov A. Yu., Rozov N. Kh., Avtovolnovye protsessy v nelineinykh sredakh s diffuziei, Fizmatlit, M., 2005

[20] Kolesov A. Yu., Rozov N. Kh., Sadovnichii V. A., “Zhizn na kromke khaosa”, Tr. sem. im. I. G. Petrovskogo, 23, 2003, 219–266 | MR | Zbl

[21] Migulin V. V., Medvedev V. I., Mustel E. R., Parygin V. N., Osnovy teorii kolebanii, M., 1988