Abstract
In this paper, we investigate the question of existence, uniqueness and bifurcation of almost periodic solutions of a non-linear ODE system with two small positive parameters and almost periodic right-hand side from the cycle of the generating system. We prove the averaging principle in the problem of almost periodic solutions of an ODE system of special type with two small parameters.
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References
Krasnosel’skii, M.A., Burd, V.Sh., Kolesov, Yu.S. Non-linear almost periodic oscillations (Nauka, Moscow, 1970) [in Russian].
Malkin, I.G. Some problems in the theory of non-linear oscillations (GITTL, Moscow, 1956) [in Russian].
Perov, A.I. “Periodic, almost periodic oscillations and bounded solutions of differential equations”, DAN SSSR 132 (3), 531–534 (1960) [in Russian].
Levitan, B.M., Zhikov, V.V. Almost periodic functions and differential equations (MSU, Moscow, 1978) [in Russian].
Tkhai, V.N. “Oscillations, stability and stabilization in the model containing coupled subsystems with cycles”, Automation and Remote Control 76 (7), 1169–1178 (2015).
Kamenski, M., Makarenko, O., Nistri, P. “A continuation principle for a class of periodically perturbed autonomous systems”, Math. Nachrichten 281 (1), 41–61 (2013).
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Russian Text © The Author(s), 2019, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, No. 6, pp. 89–92.
Submitted by V. G. Zvyagin
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Pismennyy, N.A. Almost Periodic Solutions of Nonlinear ODE Systems with Two Small Parameters. Russ Math. 63, 82–84 (2019). https://doi.org/10.3103/S1066369X19060100
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DOI: https://doi.org/10.3103/S1066369X19060100