THE COMPARATIVE ANALYSIS OF SYNCHRONIZATION BY A HARMONIOUS AND PULSE FORCE BY THE EXAMPLE OF LORENTZ SYSTEM


Cite this article as:

Aidarova Y. S., Kuznetsov A. P., Turukina L. V. THE COMPARATIVE ANALYSIS OF SYNCHRONIZATION BY A HARMONIOUS AND PULSE FORCE BY THE EXAMPLE OF LORENTZ SYSTEM. Izvestiya VUZ. Applied Nonlinear Dynamics, 2007, vol. 15, iss. 4, pp. 55-67. DOI: https://doi.org/10.18500/0869-6632-2007-15-4-​55-67


The synchronization by external periodic force of Lorenz system is under both numeric and analytical investigation in this paper. Properly studied the changes in synchronization caused by alteration of parameter value, which is responsible for arising of chaotic attractor in autonomous system.

 

Key words: 
-
DOI: 
10.18500/0869-6632-2007-15-4-​55-67
Literature

1. Неймарк Ю.И., Ланда П.С. Стохастические и хаотические колебания. М.: Наука, 1987.

2. Берже П., Помо И., Видаль К. Порядок в хаосе. М.: Мир, 1991.

3. Ott E. Chaos in dynamical systems. Cambridge university press, 1993.

4. Анищенко В.С. Сложные колебания в простых системах. М.: Наука, 1990.

5. Winfree A.T. The Geometry of Biological Time. Springer Berlin, 1980.

6. Пиковский А., Розенблюм М., Куртс Ю. Синхронизация. Фундаментальное нелинейное явление. М.: Техносфера, 2003.

7. Mosekilde E., Maistrenko Yu., Postnov D. Chaotic synchronization: applications to living systems. Singapore: World Scientific. 2002.

8. Kuramoto Y. Chemical oscillations, waves and turbulence. Berlin: Springer-Verlag. 1984.

9. Caldas I.L., Tasson H. Limit cycles of periodically forced oscillations // Phys. Lett., 1989. Vol. A135. P. 264.

10. Steeb W.H., Kunick A. Chaos in limit-cycle systems with external periodic excitation // Int. J of Nonlinear Mechanics. 1987. No 22. P. 349.

11. Glass L., Sun J. Periodic forcing of a limit-cycle oscillator: Fixed points, Arnold tongues, and the global organization of bifurcations // Phys. Rev. 1994. Vol. 50, No 6. P. 5077.

12. Pecora L. and Carroll T. Synchronization in chaotic systems // Phys. Rev. Lett. 1990. Vol. 64. P. 821.

13. Dykman G., Landa P. and Neimark Y. Synchronizing the chaotic oscillations by external force // Chaos, Solitons and Fractals. 1992. Vol. 1. P. 339.

14. Anishchenko V.S., Vadivasova T.E., Postnov D.E. and Safonova M.A. Synchronization of chaos //. Int. J. Bifurcation and Chaos. 1992. Vol. 2. P. 633.

15. Anishchenko V.S., Silchenko A.N. and Khovanov I.A. Synchronization of switching processes in coupled Lorenz systems // Phys. Rev. E. 1998. Vol. 57. P. 316.

16. Rosenblum M., Pikovsky A. and Kurths J. Phase synchronization of chaotic oscillators // Phys. Rev. Lett. 1996. Vol. 76. P. 1804.

17. Кузнецов С.П. Динамический хаос. М.: Физматлит, 2001.

18. E. Lorenz. Deterministic Nonperiodic Flow // Journal of Atmospheric Sciences. 1963. Vol. 20. P. 130.

19. Park E.-H., Zaks M.A., Kurths J. Phase synchronization in the forced Lorenz system // Phys. Rev. E. 1999. Vol. 60. P. 6627.

20. Кузнецов Ю.И., Ланда П.С. и др. Связь между амплитудным порогом синхронизации и энтропией в стохастических автоколебательных системах // Доклады Академии наук СССР. 1985. T. 281, No 2. с. 291.

21. Ланда П.С., Рендель Ю.С., Шер В.А. Синхронизация колебаний в системе Лоренца // Известия вузов: Радиофизика. 1989. Т. 32, No 9. C. 1172.

22. Афанасьев В.В., Польский И.С. и др. Применение метода Мельникова для оценки эффективности влияния внешних воздействий на сложные нелинейные системы со странными аттракторами // Письма в ЖТФ. 1997. Т. 23, No 23.

Status: 
одобрено к публикации
Short Text (PDF): 
Full Text (PDF): 

BibTeX

@article{Айдарова -IzvVUZ_AND-15-4-55,
author = {Yu. S. Aidarova and A. P. Kuznetsov and L. V. Turukina},
title = {THE COMPARATIVE ANALYSIS OF SYNCHRONIZATION BY A HARMONIOUS AND PULSE FORCE BY THE EXAMPLE OF LORENTZ SYSTEM},
year = {2007},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {15},number = {4},
url = {https://old-andjournal.sgu.ru/en/articles/the-comparative-analysis-of-synchronization-by-harmonious-and-pulse-force-by-the-example-of},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2007-15-4-​55-67},pages = {55--67},issn = {0869-6632},
keywords = {-},
abstract = {The synchronization by external periodic force of Lorenz system is under both numeric and analytical investigation in this paper. Properly studied the changes in synchronization caused by alteration of parameter value, which is responsible for arising of chaotic attractor in autonomous system.   }}