SYNCHRONIZATION OF TWO-FREQUENCY QUASI-PERIODIC OSCILLATIONS
Cite this article as:
Anishenko V. S., Nikolaev S. М. SYNCHRONIZATION OF TWO-FREQUENCY QUASI-PERIODIC OSCILLATIONS. Izvestiya VUZ. Applied Nonlinear Dynamics, 2008, vol. 16, iss. 2, pp. 69-86. DOI: https://doi.org/10.18500/0869-6632-2008-16-2-69-86
In present paper we study the effect of synchronization of two-frequency quasiperiodic oscillations. We analyze both external and mutual synchronization. The peculiarities of synchronization of a resonant limit cycle on a two-dimensional torus are established. It is shown that in general case, one and then another one of the basic frequencies is locked. The results of computer simulation are confirmed experimentally.
1. Ruelle D., Takens F. On the nature of turbulence // Commun. Math. Phys. 1971. Vol. 20. P. 167.
2. Newhouse S., Ruelle D., Takens F. Occurrence of strange axiom A attractors near quasi-periofic flows on T
3. Franceshini V. Bifurcations of tori and phase locking in a dissipative system of differential equations // Physica D. 1983. Vol. 3. P. 285.
4. Kaneko K. Collapse of tori and genesis of chaos in dissipative systems. World Scientific, Singapore, 1986.
5. Афраймович В.С., Шильников Л.П. Методы качественной теории дифференциальных уравнений // Горький: Изд-во ГГУ, 1983. С. 3.
6. Гонченко С.В., Стенькин О.В., Шильников Л.П. О существовании счетного множества устойчивых и неустойчивых инвариантных торов у систем из областей Ньюхауса с гетероклиническими касаниями // Нелинейная динамика. 2006. Т. 2, No 1. С. 3.
7. Anishchenko V., Nikolaev S., Kurths J. Winding number locking on a two-dimensional torus: Synchronization of quasi-periodic motions // Phys. Rev. E. 2006. Vol. 73. 056202.
8. Anishchenko V., Nikolaev S., Kurths J. Peculiarities of synchronization of a resonant limit cycle on a two-dimensional torus // Phys. Rev. E. 2007. Vol. 76. 046216.
9. Анищенко В.С., Николаев С.М., Kurths J. Механизмы синхронизации резонансного предельного цикла на двумерном торе // Нелинейная динамика. 2008. Т. 4, No 1. С. 39. m, m ≥ 3 // Commun. Math. Phys. 1978. Vol. 64. P. 35.
10. Анищенко В.С., Николаев С.М. Экспериментальное исследование синхронизации двухчастотных квазипериодических колебаний // Изв. вузов. Прикладная нелинейная динамика. 2007. Т. 15, No 6. С. 93.
BibTeX
author = {Vadim S. Anishenko and S. М. Nikolaev},
title = {SYNCHRONIZATION OF TWO-FREQUENCY QUASI-PERIODIC OSCILLATIONS},
year = {2008},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {16},number = {2},
url = {https://old-andjournal.sgu.ru/en/articles/synchronization-of-two-frequency-quasi-periodic-oscillations},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2008-16-2-69-86},pages = {69--86},issn = {0869-6632},
keywords = {-},
abstract = {In present paper we study the effect of synchronization of two-frequency quasiperiodic oscillations. We analyze both external and mutual synchronization. The peculiarities of synchronization of a resonant limit cycle on a two-dimensional torus are established. It is shown that in general case, one and then another one of the basic frequencies is locked. The results of computer simulation are confirmed experimentally. }}