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Russian Academy of Sciences
in January 1936
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IssuesArchive of Issues2010-4pp.389-400

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D.A. Kulikov, "Self-similar cycles and their local bifurcations in the problem of two weakly coupled oscillators," J. Appl. Math. Mech. 74 (4), 389-400 (2010)
Year 2010 Volume 74 Issue 4 Pages 389-400
Title Self-similar cycles and their local bifurcations in the problem of two weakly coupled oscillators
Author(s) D.A. Kulikov (Yaroslavl, Russia,
Abstract A system of two non-linear differential equations is considered that simulates the dynamics of two completely identical weakly coupled oscillators both in the case of dissipative and active coupling. The system of normal modes is investigated. All the self-similar periodic solutions, including the asymmetric solutions describing the natural ascillations of oscillators with dissimilar amplitude's, are found analytically. The stability is investigated as well as the local bifurcations of the self-similar cycles when there is a change in stability. In particular, the possibility of the creation of two-dimensional invariant tori is pointed out. In the case of active coupling, it is shown that the basic version of the natural oscillations is a stable antiphase cycle that was observed in Huygens experiments.
Received 6 November 2008
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