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Matematicheskie Zametki, 2020, Volume 107, Issue 6, Pages 833–847
DOI: https://doi.org/10.4213/mzm12495 (Mi mzm12495) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Relaxation Oscillations in a Logistic Equation with Nonconstant Delay

V. O. Golubenets

P.G. Demidov Yaroslavl State University
Full-text PDF (631 kB) Citations (7)
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DOI: https://doi.org/10.4213/mzm12495
Abstract: A logistic equation with state- and parameter-dependent delay is considered. The existence of a nonlocal relaxation periodic solution of this equation is proved for sufficiently large parameter values. The proof is carried out by using the large parameter method. For large parameter values, asymptotic estimates of the main characteristics of this solution are also constructed.
Keywords: delay equation, relaxation solution, large parameter method.
Funding agency Grant number
Russian Foundation for Basic Research 19-31-90082
This work was supported by the Russian Foundation for Basic Research under grant 19-31-90082.
Received: 26.06.2019
English version:
Mathematical Notes, 2020, Volume 107, Issue 6, Pages 920–932
DOI: https://doi.org/10.1134/S0001434620050223
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: V. O. Golubenets, “Relaxation Oscillations in a Logistic Equation with Nonconstant Delay”, Mat. Zametki, 107:6 (2020), 833–847; Math. Notes, 107:6 (2020), 920–932
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm12495
  • https://doi.org/10.4213/mzm12495
  • https://www.mathnet.ru/eng/mzm/v107/i6/p833
    • This publication is cited in the following 7 articles:
    1. A. Kashchenko, S. Kashchenko, “Relaxation oscillations in the logistic equation with delay and modified nonlinearity”, Mathematics, 11:7 (2023), 1699  crossref
    2. N. T. Levashova, N. A. Mikheev, “Cauchy problem for a singularly perturbed delay equation”, Moscow Univ. Phys., 78:5 (2023), 595  crossref  crossref
    3. I. S. Kashchenko, E. M. Glushevskii, “Local dynamics of equation with periodically distributed delay”, Theoret. and Math. Phys., 212:2 (2022), 1125–1136  mathnet  crossref  crossref  mathscinet  adsnasa
    4. I. Kashchenko, “Endless process of bifurcations in delay differential equations”, Int. J. Bifurcation Chaos, 32:13 (2022)  crossref
    5. V. O. Golubenets, “Relaxation oscillations in a logistic equation with past state-dependent delay”, Theoret. and Math. Phys., 207:3 (2021), 738–750  mathnet  crossref  crossref  adsnasa  isi  elib
    6. I. S. Kashchenko, E. V. Krivets, “Dynamics of a singularly perturbed system of two differential equations with delay”, Theoret. and Math. Phys., 207:3 (2021), 770–781  mathnet  crossref  crossref  adsnasa  isi  elib
    7. S. A. Kashchenko, “Bifurcating solutions and asymptotics in logistic equation with state-dependent delays”, Int. J. Bifurcation Chaos, 31:11 (2021), 2150172  crossref  mathscinet  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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