Algorithm for constructing asymptotics of periodic solutions in laser models with a rapidly oscillating delay
https://doi.org/10.18255/1818-1015-2025-1-6-15
Abstract
The problem of stability of the equilibrium state in a laser system with fast oscillating coefficients is considered. A system averaged over fast oscillations and with a distributed delay is constructed. Critical cases in the problem of the stability of the equilibrium state are singled out. It is shown that the threshold value of the feedback coefficient at which the equilibrium state becomes unstable increases due to rapid oscillations compared to the corresponding value in the absence of modulation. In critical cases, normal forms are constructed – equations for the slowly varying amplitude of the periodic solutions. The conditions for the existence, stability and instability of cycles are revealed.
Supporting agencies: This work was carried out within the framework of a development programme for the Regional Scientific and Educational Mathematical Center of the Yaroslavl State University with financial support from the Ministry of Science and Higher Education of the Russian Federation (Agreement on provision of subsidy from the federal budget No. 075-02-2024-1442).
About the Authors
Elena V. Grigorieva
Belarus State Economic University
Russian Federation
Russian Federation
Dmitry V. Glazkov
P.G. Demidov Yaroslavl State University
Russian Federation
Russian Federation
Anna O. Tolbey
P.G. Demidov Yaroslavl State University
Russian Federation
Russian Federation
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Review
For citations:
Grigorieva E.V., Glazkov D.V., Tolbey A.O. Algorithm for constructing asymptotics of periodic solutions in laser models with a rapidly oscillating delay. Modeling and Analysis of Information Systems. 2025;32(1):6-15. (In Russ.) https://doi.org/10.18255/1818-1015-2025-1-6-15
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