Geodesic
Chaos of 'split torus' type in three-dimensional relaxation systems
Sbornik. Mathematics, Tome 188 (1997) no. 11, pp. 1571-1586 Cet article a éte moissonné depuis la source Math-Net.Ru

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For a three-dimensional singularly perturbed system of ordinary differential equations with two slow variables and one fast variable conditions are indicated under which stochastic behaviour of the solutions is observed. This phenomenon is called chaos of 'split torus' type. 
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A. Yu. Kolesov; Yu. S. Kolesov; N. Kh. Rozov. Chaos of 'split torus' type in three-dimensional relaxation systems. Sbornik. Mathematics, Tome 188 (1997) no. 11, pp. 1571-1586. http://geodesic.mathdoc.fr/item/SM_1997_188_11_a0/

[1] Hutchinson G. E., “Circular causal systems in ecology”, Ann. N. Y. Acad. of Sci., 50 (1948), 221–246 | DOI

[2] Pikovskii A. S., Rabinovich M. I., “Prostoi avtogenerator so stokhasticheskim povedeniem”, Dokl. AN SSSR, 239:2 (1978), 301–304 | MR

[3] Chentsova N. N., “Issledovanie odnoi modelnoi sistemy kvazistokhasticheskikh relaksatsionnykh kolebanii”, UMN, 37:5 (1982), 205–206 | MR | Zbl

[4] Chentsova N. N., “Issledovanie kvazistokhasticheskogo rezhima avtogeneratora na tunnelnom diode”, Metody kachestvennoi teorii differentsialnykh uravnenii, Izd-vo GGU, Gorkii, 1983, 95–118 | MR

[5] Kolesov A. Yu., Kolesov Yu. S., Mischenko E. F., Rozov N. Kh., “O yavleniyakh khaosa v trekhmernykh relaksatsionnykh sistemakh”, Matem. zametki, 46:2 (1989), 153–155 | MR | Zbl

[6] Mischenko E. F., Kolesov Yu. S., Kolesov A. Yu., Rozov N. Kh., Periodicheskie dvizheniya i bifurkatsionnye protsessy v singulyarno vozmuschennykh sistemakh, Fizmatlit, M., 1995 | MR

[7] Mischenko E. F., Rozov N. Kh., Differentsialnye uravneniya s malym parametrom i relaksatsionnye kolebaniya, Fizmatlit, M., 1975

[8] Vasileva A. B., Butuzov V. F., Asimptoticheskie razlozheniya reshenii singulyarno vozmuschennykh uravnenii, Fizmatlit, M., 1973 | MR

[9] Mitropolskii Yu. A., Lykova O. B., Integralnye mnogoobraziya v nelineinoi mekhanike, Fizmatlit, M., 1973 | MR | Zbl

[10] Kolesov A. Yu., “Spetsificheskie relaksatsionnye tsikly sistem tipa Lotki–Volterra”, Izv. AN SSSR. Ser. matem., 55:3 (1991), 515–536 | MR

[11] Shilnikov L. P., “Ob odnoi zadache Puankare–Birgofa”, Matem. sb., 74:3 (1967), 378–397 | MR | Zbl

[12] Khartman F., Obyknovennye differentsialnye uravneniya, Mir, M., 1970 | MR | Zbl

[13] Mischenko E. F., Pontryagin L. S., “Periodicheskie resheniya sistem differentsialnykh uravnenii, blizkikh k razryvnym”, Dokl. AN SSSR, 102:5 (1955), 889–891 | MR | Zbl

[14] Kolesov A. Yu., Kolesov Yu. S., Mischenko E. F., Rozov N. Kh., “Asimptoticheskoe integrirovanie sistemy v variatsiyakh mnogomernogo relaksatsionnogo tsikla. I; II”, Differents. uravn., 23:11 (1987), 1881–1889 ; 12, 2036–2047 | MR | MR | Zbl

[15] Kolesov A. Yu., Kolesov Yu. S., Mischenko E. F., Rozov N. Kh., “Relaksatsionnaya sistema v okrestnosti tochki sryva: svedenie k regulyarnomu sluchayu”, UMN, 43:2 (1988), 141–142 | MR

[16] Kolesov A. Yu., Mischenko E. F., “Asimptotika relaksatsionnykh kolebanii”, Matem. sb., 137:1 (1988), 3–18

[17] Mischenko E. F., Kolesov A. Yu., “Asimptoticheskaya teoriya relaksatsionnykh kolebanii”, Trudy MIAN SSSR, 197, Nauka, M., 1991, 3–84 | Zbl