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Teoreticheskaya i Matematicheskaya Fizika, 2021, Volume 207, Number 3, Pages 389–402
DOI: https://doi.org/10.4213/tmf10042 (Mi tmf10042) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Relaxation oscillations in a logistic equation with past state-dependent delay

V. O. Golubenets

Demidov Yaroslavl State University, Yaroslavl, Russia
Full-text PDF (565 kB) Citations (3)
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DOI: https://doi.org/10.4213/tmf10042
Abstract: A logistic equation with a delay depending on the state in the past is considered. We study the question of the existence of nonlocal relaxation periodic solutions of this equation for large values of the parameter. The characteristics (for example, period and extreme values) of solutions that we find are compared with similar characteristics of solutions of other modifications of this equation. Asymptotic estimates for the period and the maximum and minimum values are obtained. The study is carried out by the large parameter method.
Keywords: delay equation, nonconstant delay, relaxation solution, asymptotics, large parameter method.
Funding agency Grant number
Russian Foundation for Basic Research 19-31-90082
This paper was supported by the Russian Foundation for Basic Research, project No 19-31-90082.
Received: 23.12.2020
Revised: 30.01.2021
English version:
Theoretical and Mathematical Physics, 2021, Volume 207, Issue 3, Pages 738–750
DOI: https://doi.org/10.1134/S0040577921060052
Bibliographic databases:
Document Type: Article
MSC: 37C99
Language: Russian
Citation: V. O. Golubenets, “Relaxation oscillations in a logistic equation with past state-dependent delay”, TMF, 207:3 (2021), 389–402; Theoret. and Math. Phys., 207:3 (2021), 738–750
Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf10042
  • https://www.mathnet.ru/eng/tmf/v207/i3/p389
    • This publication is cited in the following 3 articles:
    1. Zheng Zhao, “Railroad freight service quality evaluation system based on a logistic regression model”, Applied Mathematics and Nonlinear Sciences, 9:1 (2024)  crossref
    2. H. Tian, K. Guo, R. Zhang, S. Shao, “Prediction of evolution behavior of Internet bottleneck delay based on improved Logistic equation”, Computer Networks, 236 (2023), 110041  crossref
    3. A. R. Humphries, B. Krauskopf, S. Ruschel, J. Sieber, “Nonlinear effects of instantaneous and delayed state dependence in a delayed feedback loop”, Discrete and Continuous Dynamical Systems - B, 27:12 (2022), 7245  crossref
    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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