TWO-PARAMETRIC BIFURCATIONAL ANALYSIS OF REGIMES OF COMPLETE SYNCHRONIZATION IN ENSEMBLE OF THREE DISCRETE-TIME OSCILLATORS
Cite this article as:
Shabunin А. V., Nikolaev S. М., Astakhov V. V. TWO-PARAMETRIC BIFURCATIONAL ANALYSIS OF REGIMES OF COMPLETE SYNCHRONIZATION IN ENSEMBLE OF THREE DISCRETE-TIME OSCILLATORS. Izvestiya VUZ. Applied Nonlinear Dynamics, 2005, vol. 13, iss. 6, pp. 24-39. DOI: https://doi.org/10.18500/0869-6632-2005-13-5-24-39
We invetsigate mechanisms of appearance and disappearance of regimes of complete synchronization of chaos in a ring of three logistic maps with symmetric diffusive coupling. Two-parametric bifurcational analysis is carried out and typical oscillating regimes and transitions between them are considered.
1. Fujisaka H., Yamada T. Stability theory of synchronized motion in coupled-oscillator system // Progress of Theoretical Physics. 1983. Vol. 69. P. 32.
2. Пиковский А.С. О взаимодействии странных аттракторов. Препринт ИПФ АН СССР. Горький, 1983.
3. Кузнецов С.П. Универсальность и подобие в поведении связанных систем Фейгенбаума // Изв. вузов. Радиофизика. 1985. Т. 28. С. 991.
4. Афраймович В.С., Веричев Н.Н., Рабинович М.И. Стохастическая синхронизация колебаний в диссипативных системах // Изв. вузов. Радиофизика. 1986. Т. 29. С. 1050.
5. Hasler M., Maistrenko Y., Popovich O. Simple example of partial synchronization of chaotic systems // Phys. Rev E. 1998. Vol. 58. P. 6843.
6. Rulkov N. F., Sushchik M. M., Tsimring L.S., Abrabanel H. D. I. Generalized synchronization of chaos in directionally coupled chaotic systems // Phys. Rev. E. 1995. Vol. 51. P. 980.
7. Abarbanel H.D.I., Rulkov N.F., Sushchik M.M. Generalized synchronization of chaos: The auxiliary system approach // Phys. Rev. E. 1996. Vol. 53. P. 4528.
8. Анищенко В.С., Вадивасова Т.Е., Постнов Д.Э., Сафонова М.А. Вынужденная и взаимная синхронизация хаоса // Радиотехника и электроника. 1991. Т. 36. C. 338.
9. Anishchenko V. S., Vadivasova T. E., Postnov D. E., Safonova M. A. Synchronization of chaos // Int. J. Bifurcation and Chaos. 1992. Vol. 2. P. 633.
10. Rosenblum M. G., Pikovsky A. S., Kurths J. Phase synchronization of chaotic oscillators // Phys. Rev. Lett. 1996. Vol. 76. P. 1804.
11. Belykh V. N., Mosekilde E. One-dimensional map lattices: synchronization, bifurcations, and chaotic structures // Phys. Rev. E. 1996. Vol. 54. P. 3196.
12. Brown R., Rulkov N. F. Synchronization of chaotic systems: transverse stability of trajectories in invariant manifolds // Chaos. 1997. Vol. 3. P. 395.
13. Andreyev Y. V., Dimitriev A. S. Conditions for global synchronization in lattices of chaotic elements with local connections // Int. J. of Bifurcation and Chaos. 1999. Vol. 9. P. 2165.
BibTeX
author = {А. V. Shabunin and S. М. Nikolaev and V. V. Astakhov},
title = {TWO-PARAMETRIC BIFURCATIONAL ANALYSIS OF REGIMES OF COMPLETE SYNCHRONIZATION IN ENSEMBLE OF THREE DISCRETE-TIME OSCILLATORS},
year = {2005},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {13},number = {6},
url = {https://old-andjournal.sgu.ru/en/articles/two-parametric-bifurcational-analysis-of-regimes-of-complete-synchronization-in-ensemble-of},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2005-13-5-24-39},pages = {24--39},issn = {0869-6632},
keywords = {-},
abstract = {We invetsigate mechanisms of appearance and disappearance of regimes of complete synchronization of chaos in a ring of three logistic maps with symmetric diffusive coupling. Two-parametric bifurcational analysis is carried out and typical oscillating regimes and transitions between them are considered. }}