Bifurcation analysis of mutual synchronization of two oscillators coupled with delay
Russian journal of nonlinear dynamics, Tome 13 (2017) no. 1, pp. 3-12.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, mutual synchronization of two limit-cycle oscillators coupled with delay is studied. The results of bifurcation analysis are presented under the assumption that the delay is small in comparison with the oscillation build-up time. The stability conditions for in-phase and anti-phase modes of synchronization are analyzed at different values of parameters. The synchronization tongues on the frequency mismatch — coupling strength plane are presented.
Mots-clés : bifurcation
Keywords: delay, coupled oscillators, synchronization.
@article{ND_2017_13_1_a0,
     author = {A. B. Adilova and S. A. Gerasimova and N. M. Ryskin},
     title = {Bifurcation analysis of mutual synchronization of two oscillators coupled with delay},
     journal = {Russian journal of nonlinear dynamics},
     pages = {3--12},
     publisher = {mathdoc},
     volume = {13},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2017_13_1_a0/}
}
TY  - JOUR
AU  - A. B. Adilova
AU  - S. A. Gerasimova
AU  - N. M. Ryskin
TI  - Bifurcation analysis of mutual synchronization of two oscillators coupled with delay
JO  - Russian journal of nonlinear dynamics
PY  - 2017
SP  - 3
EP  - 12
VL  - 13
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2017_13_1_a0/
LA  - ru
ID  - ND_2017_13_1_a0
ER  - 
%0 Journal Article
%A A. B. Adilova
%A S. A. Gerasimova
%A N. M. Ryskin
%T Bifurcation analysis of mutual synchronization of two oscillators coupled with delay
%J Russian journal of nonlinear dynamics
%D 2017
%P 3-12
%V 13
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2017_13_1_a0/
%G ru
%F ND_2017_13_1_a0
A. B. Adilova; S. A. Gerasimova; N. M. Ryskin. Bifurcation analysis of mutual synchronization of two oscillators coupled with delay. Russian journal of nonlinear dynamics, Tome 13 (2017) no. 1, pp. 3-12. http://geodesic.mathdoc.fr/item/ND_2017_13_1_a0/

[1] Landa P. S., Nonlinear oscillations and waves in dynamical systems, Math. Appl., 360, Springer, Dordrecht, 2013, XV, 544 pp. | MR | MR

[2] Pikovsky A., Rosenblum M., Kurths J., Synchronization: A universal concept in nonlinear sciences, Cambridge Univ. Press, New York, 2001, 432 pp. | MR | Zbl

[3] Anishchenko V., Astakhov V., Neiman A., Vadivasova T., Schimansky-Geier L., Nonlinear dynamics of chaotic and stochastic systems: Tutorial and modern developments, Springer Series in Synergetics, Springer, Berlin, 2007, XIII, 446 pp. | MR | Zbl

[4] Kuznetsov A. P., Kuznetsov S. P., Ryskin N. M., Nonlinear oscillations, 2nd ed., Fizmatlit, Moscow, 2005 (Russian)

[5] Balanov A., Janson N., Postnov D., Sosnovtseva O., Synchronization: From simple to complex, Springer Series in Synergetics, Springer, Berlin, 2009, 426 pp. | MR | Zbl

[6] York R. A., Compton R. C., “Quasi-optical power combining using mutually synchronized oscillator arrays”, IEEE Trans. Microwave Theory Tech., 39:6 (1991), 1000–1009 | DOI

[7] Rozental R. M., Ginzburg N. S., Glyavin M. Yu., Sergeev A. S., Zotova I. V., “Mutual synchronization of weakly coupled gyrotrons”, Phys. Plasmas, 22:9 (2015), 093118, 5 pp. | DOI

[8] Klinshov V. V., Nekorkin V. I., “Synchronization of delay-coupled oscillator networks”, Physics–Uspekhi, 56:12 (2013), 1217–1229 | DOI

[9] Usacheva S. A., Ryskin N. M., “Phase locking of two limit cycle oscillators with delay coupling”, Chaos, 24:2 (2014), 023123, 9 pp. | DOI | MR | Zbl

[10] Aronson D. G., Ermentrout G. B., Kopell N., “Amplitude response of coupled oscillators”, Phys. D, 41:3 (1990), 403–449 | DOI | MR | Zbl

[11] Kuznetsov A. P., Stankevich N. V., Turukina L. V., “Coupled van der Pol – Duffing oscillators: Phase dynamics and structure of synchronization tongues”, Phys. D, 238:14 (2009), 1203–1215 | DOI | MR | Zbl

[12] http://www.math.pitt.edu/b̃ard/xpp/xpp.html

[13] Wirkus S., Rand R., “The dynamics of two coupled van der Pol oscillators with delay coupling”, Nonlinear Dynamics, 30:3 (2002), 205–221 | DOI | MR | Zbl

[14] Balanov A. G., Janson N. B., Astakhov V. V., McClintock P. V. E., “Role of saddle tori in the mutual synchronization of periodic oscillations”, Phys. Rev. E, 72:2 (2005), 026214, 6 pp. | DOI | MR