AUTOOSCILLATING SYSTEM WITH COMPENSATED DISSIPATION: DYNAMICS OF APPROXIMATED DISCRETE MAP
Cite this article as:
Kuznetsov A. P., Kuznetsov S. P., Savin А. V., Savin D. V. AUTOOSCILLATING SYSTEM WITH COMPENSATED DISSIPATION: DYNAMICS OF APPROXIMATED DISCRETE MAP. Izvestiya VUZ. Applied Nonlinear Dynamics, 2008, vol. 16, iss. 5, pp. 127-138. DOI: https://doi.org/10.18500/0869-6632-2008-16-5-127-138
The pulse-driven van der Pol oscillator with the external pulse amplitude depending on the system variables is considered. The discrete map for values of the system variables just before the pulse moment was obtained by the slow-varying-amplitude method. Further the parameter space of this map was analyzed, and the existence of the Hamiltonian critical behavior in this system was shown. The remarkable fact is that our system is the system with the dissipation depending not only on the parameter values, but on the variable values too. Also the existence of the quasi-periodicity and the synchronization near the unstable cycle was shown.
1. Кузнецов С.П. Динамический хаос. М.: Физматлит, 2006.
2. Шустер Г. Детерминированный хаос. М.: Мир, 1988.
3. Feigenbaum M.J. Quantitative universality for a class of nonlinear transformations // Journal of Statistical Physics. 1978. Vol. 19, No 1. P. 25.
4. Лихтенберг А., Либерман М. Регулярная и стохастическая динамика. М.: Мир, 1984.
5. MacKay R.S. In «Long Time Predictions in Dynamics», J. Wiley and Sons, New York, 1983.
6. Kuznetsov A.P., Kuznetsov S.P., Sataev I.R. A variety of period-doubling universality classes in multiparameter analysis of transition to chaos //Physica D. 1997. Vol. 109. P. 91.
7. Chen C., Gyorgyi G. and Schmidt G. Universal scaling in dissipative systems // Physical Review A. 1987. Vol. 35, No 6. P. 2660.
8. Reick C. Universal corrections to parameter scaling in period-doubling systems: Multiple scaling and crossover // Physical Review A. 1992. Vol. 45, No 2. P. 777.
9. Reinout G., Quispel W. Analytical crossover results for the Feigenbaum constants: Crossover from conservative to dissipative systems //Physical Review A. 1985. Vol. 31, No 6. P. 3924.
10. Кузнецов А.П., Кузнецов С.П., Рыскин Н.М. Нелинейные колебания. М.: Физматлит, 2002.
11. Lima R., Pettini M. Suppression of chaos by resonant parametric perturbations // Phys. Rev. A. 1990. Vol. 41, No 2. P. 726.
12. Кузнецов А.П., Тюрюкина Л.В. Синхронизация в системе с неустойчивым циклом, инициированная внешним сигналом //Письма в ЖТФ. 2003. Vol. 29. Вып. 8. С. 52.
13. Кузнецов А.П., Тюрюкина Л.В. Инициированные короткими импульсами устойчивые квазипериодические и периодические режимы в системе с неустойчивым предельным циклом //Изве. вузов. Прикладная нелинейная динамика. 2006. Vol. 14, No 1. С. 72.
14. Кузнецов А.П., Роман Ю.П., Станкевич Н.В., Тюрюкина Л.В. Синхронизация импульсами и синхронизация в связанных системах: новые аспекты классической задачи // Изв. вузов. Прикладная нелинейная динамика. 2008. No 3. C. 88.
15. Kim S.Y. Bicritical behavior of period doublings in unidirectionally coupled maps //Physical Review E. 1999. Vol. 59, No 6. P. 6585.
BibTeX
author = {A. P. Kuznetsov and Sergey P. Kuznetsov and А. V. Savin and D V. Savin},
title = {AUTOOSCILLATING SYSTEM WITH COMPENSATED DISSIPATION: DYNAMICS OF APPROXIMATED DISCRETE MAP},
year = {2008},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {16},number = {5},
url = {https://old-andjournal.sgu.ru/en/articles/autooscillating-system-with-compensated-dissipation-dynamics-of-approximated-discrete-map},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2008-16-5-127-138},pages = {127--138},issn = {0869-6632},
keywords = {-},
abstract = {The pulse-driven van der Pol oscillator with the external pulse amplitude depending on the system variables is considered. The discrete map for values of the system variables just before the pulse moment was obtained by the slow-varying-amplitude method. Further the parameter space of this map was analyzed, and the existence of the Hamiltonian critical behavior in this system was shown. The remarkable fact is that our system is the system with the dissipation depending not only on the parameter values, but on the variable values too. Also the existence of the quasi-periodicity and the synchronization near the unstable cycle was shown. }}