For citation:
Kuznetsov A. P., Milovanov S. V. Synchronization in thе system with both stable and unstable limit cycles collision bifurcation. Izvestiya VUZ. Applied Nonlinear Dynamics, 2003, vol. 11, iss. 4, pp. 16-30. DOI: 10.18500/0869-6632-2003-11-4-16-30
This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
(downloads: 0)
Language:
Russian
Article type:
Article
UDC:
517.9
Synchronization in thе system with both stable and unstable limit cycles collision bifurcation
Autors:
Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Milovanov Sergey Viktorovich, Saratov State University
Abstract:
The paper deals with the system where stable and unstable limit cycles collision bifurcation occurs. The approximate and precise study are carried out, the parameter planes and phase portraits are also presented. The possibility of synchronization above the threshold of cycles-collision bifurcation is discovered.
Key words:
Acknowledgments:
This work was supported by the Russian Foundation for Basic Research, grant 03-02-16074.
Reference:
- Rabinovich MI, Trubetskov DI. Introduction to the Theory of Oscillations and Waves. Moscow: Nauka; 1984. 432 p. (in Russian).
- Anishchenko VS, Vadivasova TE, Astakhov VV. Nonlinear Dynamics of Chaotic and Stochastic Systems. Saratov: Saratov University Publishing; 1999. 368 p. (in Russian).
- Uezu Т. Topology in dynamical systems. Physics Letters А. 1938;93(4):161-166. DOI: 10.1016/0375-9601(83)90038-5.
- Van der Pol В. Theory of the amplitude of free and forced triode vibration. Radio Rev. 1920; 1:701-710.
- Guckenheimer J, Holmes PJ. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. NY: Springer; 1993. 462 p. DOI: 10.1007/978-1-4612-1140-2.
- Mettin R, Parlitz U, Lauterborn W. Bifurcation structure оf the driven Van der Pol oscillator. International Journal оf Bifurcation ап Chaos. 1993;3(6):1529-1555. DOI: 10.1142/S0218127493001203.
- Parlitz U. Common dynamical features of periodically driven strictly dissipative oscillators. International Journal оf Bifurcation ап Chaos. 1993;3(3):703-715. DOI: 10.1142/S0218127493000611.
- Dumortier F, Rousseau С. Cubic Lienard equation with linear damping. Nonlinearity 1990;3(4):1015-1039. DOI: 10.1088/0951-7715/3/4/004.
- Glenndinning P, Proctor M. Travelling waves with spatially resonant forcing: bifurcations оf а modified Landau equation. International Journal оf Bifurcation and Chaos. 1993;3(6):1447-1455. DOI: 10.1142/S0218127493001148.
- Kuznetsov AP, Kuznetsov SP, Ryskin NM. Nonlinear Oscillations. Moscow: Fizmatlit; 2002. 292 p. (in Russian).
- Arnold VI. Catastrophe Theory. Berlin: Springer; 1986. 108 p. DOI: 10.1007/978-3-642-96937-9.
Received:
27.02.2003
Accepted:
29.04.2003
Available online:
29.11.2023
Published:
31.12.2003
Journal issue:
- 303 reads