Abstract:
The delay logistic equation with rapidly oscillating coefficients is studied. An averaged equation is constructed, and its dynamics is investigated. Algorithms relating the dynamical modes of the original and averaged equations are developed. It is established that the solutions are particularly sensitive to the choice of functions describing the oscillations of the delay coefficient.
Keywords:
averaging, stability, normal forms, bifurcations, asymptotics.
Citation:
S. A. Kashchenko, “Application of the Averaging Principle to the Study of the Dynamics of the Delay Logistic Equation”, Mat. Zametki, 104:2 (2018), 216–230; Math. Notes, 104:2 (2018), 231–243
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\by S.~A.~Kashchenko
\paper Application of the Averaging Principle to the Study of the Dynamics of the Delay Logistic Equation
\jour Mat. Zametki
\yr 2018
\vol 104
\issue 2
\pages 216--230
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\jour Math. Notes
\yr 2018
\vol 104
\issue 2
\pages 231--243
\crossref{https://doi.org/10.1134/S0001434618070246}
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Linking options:
https://www.mathnet.ru/eng/mzm11704
https://doi.org/10.4213/mzm11704
https://www.mathnet.ru/eng/mzm/v104/i2/p216
This publication is cited in the following 4 articles:
S. A. Kaschenko, “Chains with Diffusion-Type Couplings Containing a Large Delay”, Math. Notes, 115:3 (2024), 323–335
Sergey Kashchenko, “Chains with Connections of Diffusion and Advective Types”, Mathematics, 12:6 (2024), 790
S. A. Kashchenko, D. O. Loginov, “Andronov–Hopf Bifurcation in Logistic Delay Equations with Diffusion and Rapidly Oscillating Coefficients”, Math. Notes, 108:1 (2020), 50–63
S. A. Kashchenko, D. O. Loginov, “Andronov–Hopf Bifurcation in Logistic Delay Equations with Diffusion and Rapidly Oscillating Coefficients”, Math Notes, 108:1-2 (2020), 50