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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 7, Pages 1070–1081
DOI: https://doi.org/10.31857/S0044466921070085
(Mi zvmmf11259)
 

This article is cited in 4 scientific papers (total in 4 papers)

Ordinary differential equations

Corporate dynamics in chains of coupled logistic equations with delay

S. A. Kaschenko

Demidov Yaroslavl State University, 150003, Yaroslavl, Russia
Citations (4)
Abstract: The local dynamics of coupled chains of identical oscillators are considered. As a basic model of an oscillator, the well-known logistic equation with delay is proposed. The transition to studying a spatially distributed model is made. Two types of coupling of major interest are treated: diffusive coupling and unidirectional coupling. Critical cases are distinguished in the stability problem for the equilibrium state. It turns out that they are of infinite dimension: infinitely many roots of the characteristic equation tend to the imaginary axis as a small parameter characterizing the inverse of the number of elements in the chain tends to zero. The main result is the constructed special nonlinear boundary value problems whose nonlocal dynamics describes the behavior of all solutions for the chain in a neighborhood of the equilibrium state.
Key words: bifurcations, stability, normal forms, singular perturbations, dynamics.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 075-02-2020-1514
This study was performed within the program for the development of the regional Scientific and Educational Mathematical Centre (Yaroslavl State University) and was supported by the Ministry of Science and Higher Education of the Russian Federation, Additional Agreement no. 075-02-2020-1514/1 to the Agreement no. 075-02-2020-1514 on the provision of subsidies from the federal budget.
Received: 14.02.2020
Revised: 26.11.2020
Accepted: 11.03.2021
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 7, Pages 1063–1074
DOI: https://doi.org/10.1134/S0965542521070083
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: S. A. Kaschenko, “Corporate dynamics in chains of coupled logistic equations with delay”, Zh. Vychisl. Mat. Mat. Fiz., 61:7 (2021), 1070–1081; Comput. Math. Math. Phys., 61:7 (2021), 1063–1074
Citation in format AMSBIB
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\pages 1063--1074
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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