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Kuznetsov A. P., Stankevich N. V., Turukina 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. Applied Nonlinear Dynamics, 2006, vol. 14, iss. 6, pp. 43-53. DOI:


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

Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Stankevich Natalija Vladimirovna, Yuri Gagarin State Technical University of Saratov
Turukina L. V., Saratov State University

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.

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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.

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