The field of a variational system and its effect on the loss of orbital stability are analyzed.
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A. A. Martynyuk and N. V. Nikitina, “On periodic motion and bifurcations in three-dimensional nonlinear systems,” J. Math. Sci., 208, No. 5, 593–606 (2015).
N. V. Nikitina, “Lyapunov characteristic exponents,” Dop. NAN Ukrainy, No. 8, 64–71 (2015).
N. V. Nikitina, Nonlinear Systems with Complex and Chaotic Behavior of Trajectories [in Russian], Feniks, Kyiv (2012).
V. S. Anishechenko, V. V. Astakhov, T. E. Vadivasova, O. V. Sosnovtseva, C. W. Wu, and L. Chua, “Dynamics of two coupled Chua’s circuits,” Int. J. Bifurc. Chaos, 5, No. 6, 1677–1699 (1995).
G. A. Leonov, Strange Attractors and Classical Stability Theory, St. Peterburg, St. Peterburg University Press (2008).
A. A. Martynyuk and N. V. Nikitina, “Bifurcations and multi-stabilty of vibrations of three-dimensional system,” Int. Appl. Mech., 51, No. 2, 540–541 (2015).
A. A. Martynyuk and N. B. Nikitina, “On periodical motions in three-dimensional systems,” Int. Appl. Mech., 51, No. 4, 369–379 (2015).
Yu. I. Neimark and P. S. Landa, Stochastic and Chaotic Oscillations, Kluwer, Dordrecht (1992).
V. V. Nemytskii and V. V. Stepanov, Qualitative Theory of Differential Equation, Princeton Univ. Press, Princeton (1960).
N. V. Nikitina and V. N. Sidorets, “Bifmurcation processes in a physical model,” Int. Appl. Mech., 52, No. 3, 326–332 (2016).
L. P. Shilnikov, A. L. Shilnikov, D. B. Turaev, and L. O. Chua, Methods of Qualitative Theory in Nonlinear Dynamics, Part I, World Scientific, Singapore (1998).
L. P. Shilnikov, A. L. Shilnikov, D. V. Turaev, and L. O. Chua, Methods of Qualitative Theory in Nonlinear Dynamics, Part II, World Scientific, Singapore (2001).
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Translated from Prikladnaya Mekhanika, Vol. 53, No. 6, pp. 121–132, November–December, 2017.
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Nikitina, N.V. Analyzing the Mechanisms of Loss of Orbital Stability in Mathematical Models of Three-Dimensional Systems. Int Appl Mech 53, 716–726 (2017). https://doi.org/10.1007/s10778-018-0853-7
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DOI: https://doi.org/10.1007/s10778-018-0853-7