@article{ZVMMF_1997_37_3_a5,
author = {V. F. Daǐludenko and A. M. Krot},
title = {Calculation of the minimal embedding dimension of a chaotic attractor on the basis of local topological analysis of phase trajectories},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {315--324},
year = {1997},
volume = {37},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_1997_37_3_a5/}
}
TY - JOUR AU - V. F. Daǐludenko AU - A. M. Krot TI - Calculation of the minimal embedding dimension of a chaotic attractor on the basis of local topological analysis of phase trajectories JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 1997 SP - 315 EP - 324 VL - 37 IS - 3 UR - http://geodesic.mathdoc.fr/item/ZVMMF_1997_37_3_a5/ LA - ru ID - ZVMMF_1997_37_3_a5 ER -
%0 Journal Article %A V. F. Daǐludenko %A A. M. Krot %T Calculation of the minimal embedding dimension of a chaotic attractor on the basis of local topological analysis of phase trajectories %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 1997 %P 315-324 %V 37 %N 3 %U http://geodesic.mathdoc.fr/item/ZVMMF_1997_37_3_a5/ %G ru %F ZVMMF_1997_37_3_a5
V. F. Daǐludenko; A. M. Krot. Calculation of the minimal embedding dimension of a chaotic attractor on the basis of local topological analysis of phase trajectories. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 37 (1997) no. 3, pp. 315-324. http://geodesic.mathdoc.fr/item/ZVMMF_1997_37_3_a5/
[1] Shuster G., Determinirovannyi khaos: Vvedenie, Mir, M., 1988 | MR | Zbl
[2] Berzhe P., Pomo I., Vidal K., Poryadok v khaose. O determinirovannom podkhode k turbulentnosti, Mir, M., 1991 | MR
[3] Malinetskii G. G., Potapov A. B., Rakhmanov A. I., Ogranicheniya vozmozhnostei rekonstruktsii attraktora dlya khaoticheskikh dinamicheskikh sistem, Preprint No 10, IPMatem. RAN, M., 1993
[4] Potapov A. B., Krivizna rekonstruktsii po vremennym ryadam i “estestvennoe vremya” dlya khaoticheskikh dinamicheskikh sistem, Preprint No 11, IPMatem. RAN, M., 1993
[5] Malinetskii G. G., Potapov A. B., “O vychislenii razmernosti strannykh attraktorov”, Zh. vychisl. matem. i matem. fiz., 28:7 (1988), 1021–1037 | MR
[6] Abarbanel H. D. I., Brown R., Sidorowich J. J., Tsimring L. Sh., “The analysis of observed chaotic data in physical systems”, Rev. Mod. Phys., 65:4 (1993), 1331–1392 | DOI | MR
[7] Nikolis G., Prigozhin I., Samoorganizatsiya v neravnovesnykh sistemakh, Mir, M., 1978
[8] Khaken G., Informatsiya i samoorganizatsiya. Makroskopicheskii podkhod k slozhnym sistemam, Mir, M., 1991 | MR
[9] Malinetskii G. G., Tsertsvadze G. Z., “Issledovanie lyapunovskogo spektra uravneniya Kuramoto–Tsuzuki”, Zh. vychisl. matem. i matem. fiz., 33:7 (1993), 1043–1053 | MR
[10] Goldberger E. L., Rigni D. R., Uest B. Dzh., “Khaos i fraktaly v fiziologii cheloveka”, V mire nauki, 1990, no. 4, 25–33
[11] Farmer J. D., Sidorowich J. J., “Predicting chaotic time series”, Phys. Rev. Letts, 59:8 (1987), 845–849 | DOI | MR
[12] Casdagli M., “Nonlinear prediction of chaotic time series”, Physica D, 35:3 (1989), 335–356 | DOI | MR | Zbl
[13] Kulikov M. A., “Ispolzovanie metodov nelineinoi dinamiki dlya vyyavleniya i opisaniya khaoticheskoi determinirovannoi sostavlyayuschei EEG”, Biofizika, 38:2 (1993), 314–322
[14] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Nauka, M., 1977
[15] Maikov A. R., Sveshnikov A. G., “Konservativnye raznostnye skhemy dlya nestatsionarnykh uravnenii Maksvella v trekhmernom sluchae”, Zh. vychisl. matem. i matem. fiz., 33:9 (1993), 1352–1367 | MR
[16] Takens F., “Detecting strange attractors in turbulence”, Dynamical Systems and Turbulence, Lect. Notes in Math., 898, Springer, Berlin, 1981, 366–381 | MR
[17] Pawelzik K., Schuster H. G., “Unstable periodic orbits and prediction”, Phys. Rev. A, 43:4 (1991), 1808–1812 | DOI
[18] Liebert W., Pawelzik K., Schuster H. G., “Optimal embedding of chaotic attractor from topological consideration”, Europhys. Letts, 14:6 (1991), 521–526 | DOI | MR
[19] Čtenys A., Pyragas K. “Estimation of the number of degrees of freedom from chaotic time series”, Phys. Letts. A, 129:4 (1988), 227–230 | DOI
[20] Sugihara G., May R. M., “Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series”, Nature, 344:6268 (1990), 734–741 | DOI
[21] Ott E., Grebogi C., Yorke J. A., “Controlling chaos”, Phys. Rev. Letts, 64:11 (1990), 1196–1199 | DOI | MR | Zbl
[22] Grassberger P., Procaccia I., “Characterization of strange attractors”, Phys. Rev. Letts, 50:5 (1983), 346–349 | DOI | MR
[23] Bauer M., Heng H., Martienssen W., “Characterization of spatiotemporal chaos from time series”, Phys. Rev. Letts, 71:4 (1993), 521–524 | DOI
[24] Casdagli M., Eubank S., Farmer J. D., Gibson J., “State space reconstruction in the presence of noise”, Physica D, 51:1–3 (1991), 52–98 | DOI | MR | Zbl
[25] Farmer J. D., “Chaotic attractor of an infinite-dimensional dynamical systems”, Physica D, 4:3 (1982), 366–393 | DOI | MR | Zbl
[26] Mackey M. C., Glass L., “Oscillation and chaos in physiological control systems”, Science, 197:4300 (1977), 287–289 | DOI