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Bifurcations in a Delay Logistic Equation Under Small Perturbations

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Abstract

In this paper, we consider dynamic properties of a delay logistic equation. In the first section, by using bifurcation methods we study the local behavior of solutions to the initial equation. We pay the main attention to studying the dependence of dynamic properties of solutions on small perturbations with a large delay. We construct special nonlinear parabolic-type equations, whose local dynamics describes the behavior of solutions in a small neighborhood of the equilibrium state of the initial equation with delay. In the second section, with the help of asymptotic methods we study an important for applications issue related to the parametric resonance under a two-frequency perturbation.

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Funding

This work was performed within the framework of the program for the development of the regional scientific and educational mathematical center (YarGU) and financially supported by the Ministry of Education and Science of the Russian Federation (Supplementary agreement no. 075-02-2020-1514/1 to the Agreement on the provision of subsidies from the federal budget no. 075-02-2020-1514).

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Authors and Affiliations

  1. P.G. Demidov Yaroslavl State University, 14 Sovetskaya str., 150000, Yaroslavl, Russia

    S. A. Kashchenko

  2. National Engineering Physics Institute “MEPhI”, 31 Kashirskoe hwy, 115409, Moscow, 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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Russian Text © The Author(s), 2020, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2020, No. 10, pp. 47–64.

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Kashchenko, S.A. Bifurcations in a Delay Logistic Equation Under Small Perturbations. Russ Math. 64, 43–58 (2020). https://doi.org/10.3103/S1066369X20100059

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  • DOI: https://doi.org/10.3103/S1066369X20100059

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