On some simple flow systems with chaotic regimes
Matematičeskoe modelirovanie, Tome 14 (2002) no. 11, pp. 63-77.

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Results of computational analysis of some nonlinear 3D-flow systems are discribed. The systems are global dissipative and demonstrate complex behaviour. Generated strange attractors may have stable quasihyperbolic attractor (type of a Lorenz «butterfly») and quasiattractors. Time bifurcations, multistable regimes and chaotization by the doubling-period cascades and by the iritermittency are found. The investigation of dynamical characteristics of the systems has been carried out numerically by the program package «Nonlinear dynamical systems» (like a problem solver environment).
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M. D. Novikov; B. M. Pavlov. On some simple flow systems with chaotic regimes. Matematičeskoe modelirovanie, Tome 14 (2002) no. 11, pp. 63-77. http://geodesic.mathdoc.fr/item/MM_2002_14_11_a6/

[1] V. S. Anischenko, Slozhnye kolebaniya v prostykh sistemakh, Nauka, M., 1990 | MR | Zbl

[2] P. S. Landa, Nelineinye kolebaniya i volny, Nauka, M., 1997 | MR

[3] A. D. Morozov, T. N. Dragunov, S. A. Boikova, O. V. Malysheva, Invariantnye mnozhestva dinamicheskikh sistem v Windows, Editorial URSS, M., 1998

[4] B. M. Pavlov, M. D. Novikov, Avtomatizirovannyi praktikum po nelineinoi dinamike (sinergetike), MGU, M., 2000

[5] G. Benettin, L. Galgani, A. Georgilli, J. M. Strelcin, “Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them. Pt. 1, 2”, Mechanica, 15:1 (1980), 9–30 | DOI | MR

[6] A. Wolf, J. B. Swift, H. L. Swinny, J. A. Vastano, “Determing Lyapunov exponents from a time series”, Physica D, 16:3 (1985), 285 | DOI | MR | Zbl

[7] A. A. Kipchatov, S. V. Podin, “Primenenie metodiki adaptivnoi filtratsii dlya opredeleniya perioda kolebanii potokovykh sistem”, Izv. vuzov. Prikladnaya nelineinaya dinamika, 5:2–3 (1997), 75–78

[8] M. D. Novikov, B. M. Pavlov, “Ob odnoi nelineinoi modeli so slozhnoi dinamikoi”, Vestnik Moskovskogo un-ta, seriya 15, vychislitelnaya matematika i kibernetika, 2000, no. 2, 3

[9] P. Berzhe, I. Pomo, K. Vidal, Poryadok v khaose, Mir, M., 1991 | MR

[10] V. I. Arnold, V. S. Afraimovich, Yu. S. Ilyashenko, L. P. Shilnikov, “Teoriya bifurkatsii”, Dinamicheskie sistemy – 5, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, ed. V. I. Arnold, VINITI, M., 1986, 5 | MR

[11] V. S. Afraimovich, “Attractors”, Nonlinear Waves, 1, eds. A. V. Gaponov, M. I. Rabinovich, J. Engelbrecht, Springer-Verlag, Berlin, Heidelberg, 1989, 6. | MR

[12] S. Smale, “Differential Dynamical Systems”, Bull. Am. Math. Soc., 73 (1967), 747 | DOI | MR | Zbl

[13] R. V. Plykin, “O giperbolicheskikh attraktorakh diffeomorfizmov”, UMN, 35:3(213) (1980), 94–104 | MR | Zbl

[14] V. S. Anischenko, T. E. Vadivasova, V. V. Astakhov, Nelineinaya dinamika khaoticheskikh i stokhasticheskikh sistem, ed. V. S. Anischenko, Izd-vo Sarat. Un-ta, Saratov, 1999