This article is cited in 4 papers

Bifurcations of resonance oscillations and optimization of the trigonometric impulse by the nonsymmetry coefficient

D. V. Kostin

Voronezh State University

Abstract: Methods are given for the approximate calculation of a branch of a resonance oscillation when it bifurcates from a stationary point and for optimizing this branch with respect to the nonsymmetry coefficient, which is defined as the ratio between the largest and the smallest values of the amplitude. It is shown that the optimal values of the base amplitudes are the coefficients of the corresponding Fejér series. The largest value of the nonsymmetry coefficient is calculated exactly.
Bibliography: 18 titles.

Keywords: smooth functional, periodic extremal, bifurcation, nonsymmetry coefficient, Fejér trigonometric series, Lyapunov-Schmidt reduction.

UDC: 517.538

MSC: 34A37, 34C23, 34C25

Received: 09.10.2015 and 26.05.2016

DOI: 10.4213/sm8616

 English version: Sbornik: Mathematics, 2016, 207:12, 1709–1728

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