Abstract
The local dynamics of a well-known model of an optoelectronic oscillator with delayed feedback is studied. In a neighborhood of zero equilibrium, normalized equations are constructed which are boundary value problems depending on a continual parameter. Asymptotic solutions of the original nonlinear system in the form of a combination of slow and fast oscillations are obtained by solving the boundary value problems. The frequencies and amplitudes of the components of these solutions are determined.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
K. Ikeda and K. Matsumoto, Physica D 29, 223–235 (1987).
Y. C. Kouomou, P. Colet, L. Larger, and N. Gastaud, Phys. Rev. Lett. 95, 203903 (2005).
M. Peil, M. Jacquot, and Y. C. Kouomou, Phys. Rev. E 79, 026208 (2009).
L. Weicker, T. Erneux, D. P. Rosin, and D. J. Gauthier, Phys. Rev. E 91, 012910 (2015).
J. H. Talla Mbé, A. F. Talla, and G. R. Goune Chengui, Phys. Rev. E 91, 012902 (2015).
I. S. Kaschenko and S. A. Kaschenko, Int. J. Bifurcation Chaos 25 (11), 1550142 (2015).
M. Bestehorn, E. V. Grigorieva, H. Haken, and S. A. Kaschenko, Physica D 145, 111–130 (2000).
E. V. Grigorieva, I. S. Kaschenko, and S. A. Kaschenko, Nonlin. Phenomena Complex Syst. 12, 309 (2012).
Author information
Authors and Affiliations
Corresponding authors
Additional information
Translated by I. Ruzanova
Rights and permissions
About this article
Cite this article
Grigorieva, E.V., Kashchenko, S.A. Slow and Fast Oscillations in a Model of an Optoelectronic Oscillator with Delay. Dokl. Math. 99, 95–98 (2019). https://doi.org/10.1134/S1064562419010022
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1064562419010022