ISSN 0869-6632 (Online)
ISSN 2542-1905 (Print)


Cite this article as:

Kuznecov A. P., Stankevich N. V., Tjurjukina L. V. Features of the synchronization picture by the pulses in the system with 3-dimensional phase space by the example of the ressler system. Izvestiya VUZ, 2006, vol. 14, iss. 6, pp. 43-53. DOI: https://doi.org/10.18500/0869-6632-2006-14-6-43-53

Language: 
Russian

Features of the synchronization picture by the pulses in the system with 3-dimensional phase space by the example of the ressler system

Autors: 
Kuznecov Aleksandr Petrovich, Saratov State University
Stankevich Natalija Vladimirovna, Yuri Gagarin State Technical University of Saratov
Tjurjukina Ljudmila Vladimirovna, Saratov State University
Abstract: 

Features of the synchronization picture in the system which limit cycle lied in threedimensional phase space are considered. By the example of Ressler system with the periodic sequence of d-Functions it is shown, that the synchronization picture essentially depends on a direction of the external force. Features of the synchronization tongues are found.

Key words: 
DOI: 
10.18500/0869-6632-2006-14-6-43-53
References: 

1. Берже П., Помо И., Видаль К. Порядок в хаосе. М.: Мир, 1991. 368 с. 2. Шустер Г. Детерминированный хаос. М.: Мир, 1990, 240с. 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. Caldas I.L., Tasson H. Limit cycles of periodically forced oscillations // Phys. Lett, 1989. Vol. A135. p.264-266. 7. Steeb W.H., Kunick A. Chaos in limit-cycle systems with external periodic excitation // Int. J of Nonlinear Mechanics, 1987. No 22. P. 349. 8. Пиковский А., Розенблюм М., Куртс Ю. Синхронизация. Фундаментальное нелинейное явление. М.: Техносфера, 2003. 9. Pikovsky A.S., Rosenblum M.G., Osipov G.V., Kurths J. Phase synchronization of chaotic oscillators by external driving // Physica, 1997. Vol. D104. P. 219. 10. Gonzalez D.L. and Piro O. Chaos in a nonlinear driven oscillator with exact solution // Phys. Rev. Lett., 1983. Vol. 50, No 12. P. 870. 11. Ding E.J. Analytic treatment of periodic orbit systematics for a nonlinear driven oscillator // Phys. Rev., 1986. Vol. A34, No 4. P. 3547. 12. Ding E.J. Analytic treatment of a driven oscillator with a limit cycle // Phys. Rev., 1987. Vol. A35, No 6. P. 2669. 13. Ding E.J. Structure of parameter space for a prototype nonlinear oscillator // Phys. Rev., 1987. Vol. A36, No 3. P. 1488. 14. Ding E.J. Structure of the parameter space for the van der Pol oscillator // Physica Scripta, 1988. Vol. 38. P. 9. 15. Ullmann K. and Caldas I.L. Transitions in the parameter space of a periodically forced dissipative system // Chaos, Solitons & Fractals, 1996. No 11. P. 1913. 16. Keener J.P., Glass L. Global bifurcation of a periodically forced nonlinear oscillator // J. Math. Biology, 1984. No 21. P. 175. 17. 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. 18. Ding E.J. and Hemmer P.C. Exact treatment of mode locking for a piecewise linear map // Journal of Statistical Physics, 1987. Vol. 46, No 1-2. P. 99. 19. Glass L. et. all. Global bifurcations of a periodically forced biological oscillator // Phys. Rev. A., 1983. No 29. P. 1348. 20. Кузнецов А.П., Тюрюкина Л.В. Осциллятор ван-дер-Поля с импульсным воздействием: от потока к отображениям // Изв. вузов. Прикладная нелинейная динамика, 2001. No 6. С. 69. 21. Кузнецов А.П., Тюрюкина Л.В. Синхронизация автоколебательной системы ван дер Поля – Дуффинга короткими импульсами // Изв. вузов. Прикладная нелинейная динамика, 2004. No 5. С. 16. 22. Кузнецов С.П. Динамический хаос. М.:Физматлит, 2001. 296 с.

Short text (in English): 
Full text: