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Matematicheskie Zametki, 2015, Volume 98, Issue 1, Pages 85–100
DOI: https://doi.org/10.4213/mzm10507 (Mi mzm10507) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Dynamics of the Logistic Equation with Delay

S. A. Kashchenkoab

a National Engineering Physics Institute "MEPhI", Moscow
b P. G. Demidov Yaroslavl State University
Full-text PDF (635 kB) Citations (11)
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DOI: https://doi.org/10.4213/mzm10507
Abstract: The logistic equation supplemented with a summand characterizing delay is considered. The local and nonlocal dynamics of this equation are studied. For equations with delay, we use the standard Andronov–Hopf bifurcation methods and the asymptotic method developed by the author and based on the construction of special evolution equations defining the local dynamics of the equations containing delay. In addition, we study the existence and methods of constructing the asymptotics of nonlocal relaxation cycles. A comparison of the results obtained with those for the Hutchinson equation and some of its generalizations is given.
Keywords: logistic equation with delay, Andronov–Hopf bifurcation, evolution equation, Hutchinson equation, relaxation cycle, slowly/rapidly oscillating solution, quasinormal form.
Received: 28.05.2014
English version:
Mathematical Notes, 2015, Volume 98, Issue 1, Pages 98–110
DOI: https://doi.org/10.1134/S0001434615070093
Bibliographic databases:
Document Type: Article
UDC: 517.929
Language: Russian
Citation: S. A. Kashchenko, “Dynamics of the Logistic Equation with Delay”, Mat. Zametki, 98:1 (2015), 85–100; Math. Notes, 98:1 (2015), 98–110
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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