Voir la notice de l'article provenant de la source Math-Net.Ru
@article{ND_2014_10_2_a0,
author = {Irina S. Dementyeva and Alexander P. Kuznetsov and Alexey V. Savin and Yuliya V. Sedova},
title = {Quasiperiodic dynamics of three coupled logistic maps},
journal = {Russian journal of nonlinear dynamics},
pages = {139--148},
publisher = {mathdoc},
volume = {10},
number = {2},
year = {2014},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ND_2014_10_2_a0/}
}
TY - JOUR AU - Irina S. Dementyeva AU - Alexander P. Kuznetsov AU - Alexey V. Savin AU - Yuliya V. Sedova TI - Quasiperiodic dynamics of three coupled logistic maps JO - Russian journal of nonlinear dynamics PY - 2014 SP - 139 EP - 148 VL - 10 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ND_2014_10_2_a0/ LA - ru ID - ND_2014_10_2_a0 ER -
%0 Journal Article %A Irina S. Dementyeva %A Alexander P. Kuznetsov %A Alexey V. Savin %A Yuliya V. Sedova %T Quasiperiodic dynamics of three coupled logistic maps %J Russian journal of nonlinear dynamics %D 2014 %P 139-148 %V 10 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/ND_2014_10_2_a0/ %G ru %F ND_2014_10_2_a0
Irina S. Dementyeva; Alexander P. Kuznetsov; Alexey V. Savin; Yuliya V. Sedova. Quasiperiodic dynamics of three coupled logistic maps. Russian journal of nonlinear dynamics, Tome 10 (2014) no. 2, pp. 139-148. http://geodesic.mathdoc.fr/item/ND_2014_10_2_a0/
[1] Anishchenko V. S., Astakhov V. V., Neiman A. B., Vadivasova T. E., Schimansky-Geier L., Nonlinear dynamics of chaotic and stochastic systems: Tutorial and modern developments, Springer Series in Synergetics, 2nd ed., Springer, Berlin, 2007, 446 pp. | MR | Zbl
[2] Mosekilde E., Maistrenko Yu., Postnov D., Chaotic synchronization: Applications to living systems, World Sci. Ser. Nonlinear Sci. Ser. A Monogr. Treatises, 42, World Sci. Publ., River Edge, N.J., 2002, 428 pp. | MR | Zbl
[3] Shuster G., Determinirovannyi khaos, Mir, M., 1988, 240 pp. | MR
[4] Berzhe P., Pomo I., Vidal K., Poryadok v khaose. O deterministskom podkhode k turbulentnosti, Mir, M., 1991, 368 pp. | MR
[5] Kuznetsov S. P., Dinamicheskii khaos, Fizmatlit, M., 2001, 296 pp.
[6] Kuznetsov A. P., Kuznetsov S. P., “Kriticheskaya dinamika odnomernykh otobrazhenii. Ch. 1: Stsenarii Feigenbauma”, Izv. vuzov. PND, 1:1 (1993), 15–32
[7] Kuznetsov S. P., “Universalnost i podobie v povedenii svyazannykh sistem Feigenbauma”, Izv. vuzov. Radiofizika, 28:8 (1985), 991–1007 | MR
[8] Kook H., Ling F. H., Schmidt G., “Universal behavior of coupled nonlinear systems”, Phys. Rev. A, 43:6 (1991), 2700–2708 | DOI | MR
[9] Kuznetsov A. P., Sedova Yu. V., Sataev I. R., “Ustroistvo prostranstva upravlyayuschikh parametrov neidentichnykh svyazannykh sistem s udvoeniyami perioda”, Izv. vuzov. PND, 12:5 (2004), 46–57 | MR | Zbl
[10] Kim S.-Y., Kook H., “Critical behavior in coupled nonlinear systems”, Phys. Rev. A, 46:8 (1992), 4467–4470 | DOI | MR
[11] Kim S.-Y., Kook H., “Period doubling in coupled maps”, Phys. Rev. E, 48:2 (1993), 785–799 | DOI | MR
[12] Kuznetsov A. P., Kuznetsov S. P., Sedova Yu. V., “O svoistvakh skeilinga identichnykh svyazannykh logisticheskikh otobrazhenii s dvumya tipami svyazi bez shuma i pod vozdeistviem shuma”, Izv. vuzov. PND, 14:5 (2006), 94–109 | Zbl
[13] Astakhov V. V., Bezruchko B. P., Erastova E. N., Seleznev E. P., “Vidy kolebanii i ikh evolyutsiya v dissipativno svyazannykh feigenbaumovskikh sistemakh”, ZhTF, 60:10 (1990), 19–26
[14] Bezruchko B. P., Smirnov D. V., Seleznev E. P., “Evolyutsiya basseinov prityazheniya attraktorov simmetrichno svyazannykh sistem s udvoeniem perioda”, Pisma v ZhTF, 21:8 (1995), 12–17
[15] Bezruchko B. P., Seleznev E. P., “Basseiny prityazheniya khaoticheskikh attraktorov v svyazannykh sistemakh s udvoeniem perioda”, Pisma v ZhTF, 23:4 (1997), 40–46 | Zbl
[16] Astakhov V., Shabunin A., Kapitaniak T., Anishchenko V., “Loss of chaos synchronization through the sequence of bifurcations of saddle periodic orbits”, Phys. Rev. Lett., 79:6 (1997), 1014–1017 | DOI
[17] Beims M. W., Rech P. C., Gallas J. A. C., “Fractal and riddled basins: Arithmetic signatures in the parameter space of two coupled quadratic maps”, Phys. A, 295:1–2 (2001), 276–279 | DOI | MR | Zbl
[18] Reick C., Mosekilde E., “Emergemce of quasiperiodicity in symmetrically coupled, identical period-doubling systems”, Phys. Rev. E, 52:2 (1995), 1418–1435 | DOI | MR
[19] Erastova E. N., Kuznetsov S. P., “O mekhanizme vozniknoveniya kvaziperiodicheskikh kolebanii v svyazannykh sistemakh Feigenbauma”, ZhTF, 61:2 (1991), 13–20 | MR | Zbl
[20] Satoii K., Aihara T., “Numerical study on a coupled-logistic map as a simple model for a predator-prey system”, J. Phys. Soc. Japan, 59:4 (1990), 1184–1198 | DOI | MR
[21] Rech P. C., Beims M. W., Gallas J. A. C., “Naimark–Sacker bifurcations in linearly coupled quadratic maps”, Phys. A, 342:1 (2004), 351–355 | DOI
[22] Rech P. C., Beims M. W., Gallas J. A. C., “Generation of quasiperiodic oscillations in pairs of coupled maps”, Chaos Solitons Fractals, 33:4 (2007), 1394–1410 | DOI | MR | Zbl
[23] Anishchenko V. S., Safonova M. A., Feudel U., Kurths J., “Bifurcations and transition to chaos through three-dimensional tori”, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 4:3 (1994), 595–607 | DOI | MR | Zbl
[24] Nikolaev S. M., Shabunin A. V., Astakhov V. V., “Multistability of partially synchronous regimes in a system of three coupled logistic maps”, Proc. Internat. Conf. «Physics and Control» (St. Petersburg, Russia, Aug 20–22), 169–173
[25] Taborov A. V., Maistrenko Yu. L., Mosekilde E., “Partial synchronization in a system of coupled logistic maps”, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10:5 (2000), 1051–1066 | DOI | MR | Zbl
[26] Tsuruda H., Shirahama H., Fukushima K., Nagadome M., Inoue M., “Chaotic transition in a three-coupled phase-locked loop system”, Chaos, 11:2 (2001), 410–416 | DOI
[27] Levanova T. A., Osipov G. V., Pikovsky A., “Coherence properties of cycling chaos”, Commun. Nonlinear Sci. Numer. Simul., 19:8 (2014), 2734–2739 | DOI | MR
[28] Rech P. C., “A coupling of three quadratic maps”, Chaos Solitons Fractals, 41:4 (2009), 1949–1952 | DOI
[29] Xavier J., Rech P., “Chaos and hyperchaos in a symmetric coupling of three quadratic maps”, J. Comp. Int. Sci., 1:3 (2010), 225–231
[30] Baesens S., Guckenheimer J., Kim S., MacKay R. S., “Three coupled oscillators: Mode locking, global bifurcations and toroidal chaos”, Phys. D, 49:3 (1991), 387–475 | DOI | MR | Zbl
[31] Kuznetsov A. P., Pozdnyakov M. V., Sedova Yu. V., “Svyazannye universalnye otobrazheniya s bifurkatsiei Neimarka–Sakera”, Nelineinaya dinamika, 8:3 (2012), 473–482
[32] Emelianova Yu. P., Kuznetsov A. P., Sataev I. R., Turukina L. V., “Synchronization and multi-frequency oscillations in the low-dimensional chain of the self-oscillators”, Phys. D, 244:1 (2013), 36–49 | DOI | Zbl
[33] Kuznetsov A. P., Kuznetsov S. P., Sataev I. R., Turukina L. V., “About Landau–Hopf scenario in a system of coupled self-oscillators”, Phys. Lett. A, 377:45–48 (2013), 3291–3295 | DOI | MR | Zbl
[34] Emelianova Yu. P., Kuznetsov A. P., Turukina L. V., Sataev I. R., Chernyshov N. Yu., “A structure of the oscillation frequencies parameter space for the system of dissipatively coupled oscillators”, Commun. Nonlinear Sci. Numer. Simul., 19:4 (2014), 1203–1212 | DOI | MR
[35] Broer H., Simó C., Vitolo R., “Quasi-periodic bifurcations of invariant circles in low-dimensional dissipative dynamical systems”, Regul. Chaotic Dyn., 16:1–2 (2011), 154–184 | MR | Zbl
[36] Broer H., Simó C., Vitolo R., “The Hopf-saddle-node bifurcation for fixed points of 3D-diffeomorphisms: The Arnol'd resonance web”, Bull. Belg. Math. Soc. Simon Stevin, 15:5 (2008), 769–787 | MR | Zbl