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Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 203, Number 1, Pages 106–118
DOI: https://doi.org/10.4213/tmf9819 (Mi tmf9819) 		 
This article is cited in 5 scientific papers (total in 5 papers)

A relay Mackey–Glass model with two delays

M. M. Preobrazhenskaya

Demidov Yaroslavl State University, Yaroslavl, Russia
Full-text PDF (525 kB) Citations (5)
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DOI: https://doi.org/10.4213/tmf9819
Abstract: We study the dynamics of the generalized Mackey–Glass equation with two delays using the large-parameter method. After a special exponential replacement of variables, a singularly perturbed equation is obtained, for which we construct a meaningful limit object, a differential–difference relay equation with two delays. We prove that the relay equation has a simple periodic solution with one interval on the period where the solution is positive. To illustrate the obtained result, we numerically analyze the original singularly perturbed equation, for which we find a solution near the periodic solution of the limit relay equation.
Keywords: differential–difference equation, Mackey–Glass equation, large parameter, Poincaré operator.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation МК-1190.2020.1
This research was supported by the President of the Russian Federation (Grant No. MK-1190.2020.1).
Received: 16.09.2019
Revised: 28.01.2020
English version:
Theoretical and Mathematical Physics, 2020, Volume 203, Issue 1, Pages 524–534
DOI: https://doi.org/10.1134/S004057792004008X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. M. Preobrazhenskaya, “A relay Mackey–Glass model with two delays”, TMF, 203:1 (2020), 106–118; Theoret. and Math. Phys., 203:1 (2020), 524–534
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf9819
  • https://doi.org/10.4213/tmf9819
  • https://www.mathnet.ru/eng/tmf/v203/i1/p106
    • This publication is cited in the following 5 articles:
    1. V. Alekseev, “Two-cluster synchronization in a fully coupled network of Mackey–Glass generators”, Partial Differential Equations in Applied Mathematics, 2024, 100930  crossref
    2. V. V. Alekseev, M. M. Preobrazhenskaia, V. K. Vorontsova, “Existence of Discrete Traveling Waves in Fully Coupled Network of Mackey–Glass Relay Generators”, Diff Equat, 60:9 (2024), 1217  crossref
    3. A. Kashchenko, “Asymptotics of solutions to a differential equation with delay and nonlinearity having simple behaviour at infinity”, Mathematics, 10:18 (2022), 3360  crossref
    4. M. M. Preobrazhenskaya, “Discrete traveling waves in a relay system of Mackey–Glass equations with two delays”, Theoret. and Math. Phys., 207:3 (2021), 827–840  mathnet  crossref  crossref  adsnasa  isi  elib
    5. M. M. Preobrazhenskaia, “Antiphase mode in a pair of Mackey-Glass type generators with two delays”, IFAC PAPERSONLINE, 54:17 (2021), 145–148  crossref  mathscinet  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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