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Corporate Dynamics in Chains of Coupled Logistic Equations with Delay

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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.

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Funding

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.

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  1. Demidov Yaroslavl State University, 150003, Yaroslavl, Russia

    S. A. Kashchenko

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  1. S. A. Kashchenko
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Correspondence to S. A. Kashchenko.

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Translated by N. Berestova

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Kashchenko, S.A. Corporate Dynamics in Chains of Coupled Logistic Equations with Delay. Comput. Math. and Math. Phys. 61, 1063–1074 (2021). https://doi.org/10.1134/S0965542521070083

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  • DOI: https://doi.org/10.1134/S0965542521070083

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