Abstract:
In this paper, a numerical scheme of constructing approximate generally periodical solutions of a complicatedtructure of a non-autonomous system of ordinary differential equations with the periodical right-hand sides on the surface of a torus is considered. The existence of such solutions as well as convergence of the method of successive approximations are shown. There are given results of the computational experiment.
Key words:
generally-periodical solution, system of ordinary differential equations, Fourier series, almost periodical solution, irrational winding of torus.
Citation:
A. N. Pchelintsev, “On constructing the generally periodical solutions of a complicated structure of a non-autonomous system of differential equations”, Sib. Zh. Vychisl. Mat., 16:1 (2013), 63–70; Num. Anal. Appl., 6:1 (2013), 54–61
\Bibitem{Pch13}
\by A.~N.~Pchelintsev
\paper On constructing the generally periodical solutions of a~complicated structure of a~non-autonomous system of differential equations
\jour Sib. Zh. Vychisl. Mat.
\yr 2013
\vol 16
\issue 1
\pages 63--70
\mathnet{http://mi.mathnet.ru/sjvm499}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3380108}
\elib{https://elibrary.ru/item.asp?id=20432516}
\transl
\jour Num. Anal. Appl.
\yr 2013
\vol 6
\issue 1
\pages 54--61
\crossref{https://doi.org/10.1134/S1995423913010072}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84874799885}
Linking options:
https://www.mathnet.ru/eng/sjvm499
https://www.mathnet.ru/eng/sjvm/v16/i1/p63
This publication is cited in the following 2 articles:
Lozi R., Pchelintsev A.N., “A New Reliable Numerical Method For Computing Chaotic Solutions of Dynamical Systems: the Chen Attractor Case”, Int. J. Bifurcation Chaos, 25:13 (2015), 1550187
A. N. Pchelintsev, “Numerical and physical modeling of the Lorenz system dynamics”, Num. Anal. Appl., 7:2 (2014), 159–167
Citation in format AMSBIB
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