@article{ZVMMF_1998_38_3_a8,
author = {T. V. Zavrazhina},
title = {Numerical simulation of routes to chaos in dissipative oscillators with one degree of freedom},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {448--456},
year = {1998},
volume = {38},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_1998_38_3_a8/}
}
TY - JOUR AU - T. V. Zavrazhina TI - Numerical simulation of routes to chaos in dissipative oscillators with one degree of freedom JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 1998 SP - 448 EP - 456 VL - 38 IS - 3 UR - http://geodesic.mathdoc.fr/item/ZVMMF_1998_38_3_a8/ LA - ru ID - ZVMMF_1998_38_3_a8 ER -
%0 Journal Article %A T. V. Zavrazhina %T Numerical simulation of routes to chaos in dissipative oscillators with one degree of freedom %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 1998 %P 448-456 %V 38 %N 3 %U http://geodesic.mathdoc.fr/item/ZVMMF_1998_38_3_a8/ %G ru %F ZVMMF_1998_38_3_a8
T. V. Zavrazhina. Numerical simulation of routes to chaos in dissipative oscillators with one degree of freedom. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 38 (1998) no. 3, pp. 448-456. http://geodesic.mathdoc.fr/item/ZVMMF_1998_38_3_a8/
[1] Anischenko B. C., Slozhnye kolebaniya v prostykh sistemakh: Mekhanizmy vozniknoveniya, struktura i svoistva dinamicheskogo khaosa v radiofizicheskikh sistemakh, Nauka, M., 1990
[2] Batalova Z. S., Ezhevskaya N. A., Dinamika ostsillyatora Duffinga, Dep. v VINITI, No 4962-V90, 1990, 22 pp.
[3] Belogorodtsev A. B., “Teoriya regulyarnogo i khaoticheskogo povedeniya slabonelineinykh ostsillyatorov s kvaziperiodicheskim vozdeistviem”, Tezisy dokl. II Vses. konf. "Nelineinye kolebaniya mekhan. sistem" (Gorkii, 1990), 30–31
[4] Gulyaev V. I., Zavrazhina T. V., “Masshtabnye svoistva periodicheskikh dvizhenii nelineinykh konservativnykh ostsillyatorov pri perekhode k khaosu”, Prikl. mekhan., 32:1 (1995), 75–81
[5] Ioss Zh., Dzhozef D., Elementarnaya teoriya ustoichivosti i bifurkatsii, Mir, M., 1983
[6] Likhtenberg A., Liberman M., Regulyarnaya i stokhasticheskaya dinamika, Mir, M., 1984
[7] Neimark Yu. I., Landa P. S., Stokhasticheskie i khaoticheskie kolebaniya, Nauka, M., 1987
[8] Shuster G., Determinirovannyi khaos, Mir, M., 1988 | Zbl
[9] Awrejcewicz J., “A route to chaos in a nonlinear oscillator with delay”, Acta Mech., 77:1–2 (1989), 111–120 | DOI | MR
[10] Feigenbaum M. J., “Universal behaviour in nonlinear systems”, Los Alamos Science, 1:1 (1980), 4–27 | MR
[11] Greene J. M., Mackay R. S., Vivaldi F., Feigenbaum M. J., “Universal behaviour in families of area– preserving maps”, Physica D, 3:3 (1981), 468–486 | DOI | MR | Zbl
[12] Helleman R. H. G., “Feigenbaum sequences in conservative and dissipative systems”, Chaos and Order in Nature, Internat. Symp. Synergetics (Bavaria, 1981), Springer, Berlin, 1981, 232–248 | Zbl
[13] Huseyin Koncay, Lin Rui, “An intrinsic multiple-scale harmonic balance method for nonlinear vibration and bifurcation problems”, Internat. J. Non-Linear Mech., 26:5 (1991), 727–740 | DOI | MR | Zbl
[14] Pei Qinyuam, Li Li, “The chaotic behaviour of a nonlinear oscillator”, Appl. Math. and Mech., 14:5 (1993), 377–387 | MR
[15] Van Doorin R., “On the transition from regular to chaotic behaviour in the Duffing oscillator”, J. Sound and Vibr., 123:2 (1988), 327–339 | DOI
[16] Yagasaki K., Sakata M., Kimura K., “Dynamics of a weakly nonlinear system subjected to combined parametric and external excitation”, Trans. ASME. J. Appl. Mech., 57:1 (1990), 209–217 | DOI | MR | Zbl
[17] Viera M. C. de Souse, Gunarathe G. H., “The trajectory scaling function for period doubling bifurcations in flows”, J. Statist. Phys., 58:5–6 (1990), 1245–1256 | DOI | MR
[18] Gulyaev V. I., Bazhenov V. A., Gotsulyak E. A. i dr., Ustoichivost periodicheskikh protsessov v nelineinykh mekhanicheskikh sistemakh, Vischa shkola, Lvov, 1983
[19] Demidovich B. P., Lektsii po matematicheskoi teorii ustoichivosti, Nauka, M., 1967
[20] Vainberg M. M., Trenogin V. A., Teoriya vetvleniya reshenii nelineinykh uravnenii, Nauka, M., 1969
[21] Everhart E., “An implicit single sequence methods for integrating orbits”, Celest. Mech., 10 (1974), 35–55 | DOI | MR | Zbl