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Teoreticheskaya i Matematicheskaya Fizika, 2021, Volume 207, Number 3, Pages 424–437
DOI: https://doi.org/10.4213/tmf10044 (Mi tmf10044) 		 
Dynamics of a singularly perturbed system of two differential equations with delay

I. S. Kashchenko, E. V. Krivets

Demidov Yaroslavl State University, Yaroslavl, Russia
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DOI: https://doi.org/10.4213/tmf10044
Abstract: We study a two-dimensional singularly perturbed system with delay, which is a simplification of models used in laser physics. We analyze several cases of a small parameter multiplying the derivative in the first equation and investigate the behavior of solutions in a neighborhood of a stationary point when the system parameters pass through bifurcation values. Methods for local asymptotic analysis are used to construct special nonlinear equations describing the structure of solutions and the asymptotic approximation of solutions of the original problem.
Keywords: dynamics, singular perturbation, asymptotics, normal form, delay.
Funding agency Grant number
Russian Foundation for Basic Research 18-29-10043
The work was supported by the Russian Foundation for Basic Research (Grant No. 18-29-10043).
Received: 24.12.2020
Revised: 25.02.2021
English version:
Theoretical and Mathematical Physics, 2021, Volume 207, Issue 3, Pages 770–781
DOI: https://doi.org/10.1134/S0040577921060076
Bibliographic databases:
Document Type: Article
MSC: 37G05
Language: Russian
Citation: I. S. Kashchenko, E. V. Krivets, “Dynamics of a singularly perturbed system of two differential equations with delay”, TMF, 207:3 (2021), 424–437; Theoret. and Math. Phys., 207:3 (2021), 770–781
Citation in format AMSBIB
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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