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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2014, Volume 7, Issue 3, Pages 23–32 (Mi vyuru141)  

Mathematical Modelling

The Form of Key Function in the Problem of Branching of Periodic Extremals with Resonance 1:1:1

E. V. Bukhonova

Voronezh State University, Voronezh, Russian Federation

Abstract: This article contains a method for calculating approximately the standardized key functions in the problem of branching of periodic extremals of a continuously differentiable action functional near its minimum. The periodic extremals of such functionals are used as a prototype for periodic oscillations of dynamical systems, ferroelectric crystal phases, nonlinear periodic waves, as so on. Recently Karpova, Kopytin, Derunova, and Sapronov studied cycle bifurcations in dynamical systems using key equations and key functions in the cases of double resonances $p_1:p_2:p_3$ with $p_1<p_2<p_3$. This article deals with the poorly understood case $p_1=p_2=p_3 = 1$. As a demonstration model, we consider an order six ODE. We use the Lyapunov–Schmidt method.

Keywords: continuously differentiable functional; extremal; circular symmetry; resonance; bifurcation; Lyapunov–Schmidt method.

DOI: https://doi.org/10.14529/mmp140302

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UDC: 517.9
MSC: 90C30
Received: 17.05.2014

Citation: E. V. Bukhonova, “The Form of Key Function in the Problem of Branching of Periodic Extremals with Resonance 1:1:1”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 7:3 (2014), 23–32

Citation in format AMSBIB
\Bibitem{Buk14}
\by E.~V.~Bukhonova
\paper The Form of Key Function in the Problem of Branching of Periodic Extremals with Resonance~1:1:1
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2014
\vol 7
\issue 3
\pages 23--32
\mathnet{http://mi.mathnet.ru/vyuru141}
\crossref{https://doi.org/10.14529/mmp140302}


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