A generator with inertial nonlinearity is considered. The bifurcations are illustrated by simple examples using the comparison method and Lyapunov functions
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References
V. S. Anishchenko, Complex Oscillations in Simple Systems [in Russian], Nauka, Moscow (1990).
S. A. Koblyanskiy, A. V. Shabunin, and V. V. Astakhov, “Forced synchronization of periodic oscillations in a system with phase multistability,” Rus. J. Nonlin. Dyn., 6, No. 2, 277–289 (2010).
A. A. Martynyuk and A. Yu. Obolenskii, “Stability of solutions of Wazewski’s autonomous systems,” Diff. Uravn., 16, No. 8, 1392–1407 (1980).
N. V. Nikitina, Nonlinear Systems with Complex and Chaotic Behavior of Trajectories [in Russian], Feniks, Kyiv (2012).
V. S. Anishchenko, S. V. Astakhov, and T. E. Vadivasova, “Diagnostics of the degree of noise influence on a nonlinear system using relative metric entropy,” Regul. Chaot. Dynam., 15, No. 2–3, 263–276 (2010).
V. A. Krys’ko, T. V. Yakovleva, V. V. Dobriyan, and I. V. Papkova, “Wavelet-analysis-based chaotic synchronization of vibrations of multilayer mechanical structures,” Int. Appl. Mech., 50, No. 6, 706–720 (2014).
G. A. Leonov, Strange Attractors and Classical Stability Theory, University Press, St. Peterburg (2008).
A. A. Martynyuk, “Asymptotic stability criterion for nonlinear monotonic systems and its applications (review),” Int. Appl. Mech., 47, No. 5, 475–534 (2011).
A. A. Martynyuk and N. V. Nikitina, “Bifurcation processes in periodically perturbed systems,” Int. Appl. Mech., 49, No. 1, 114–121 (2013).
A. A. Martynyuk and N. V. Nikitina, “Stability and bifurcation in a model of the magnetic field of the Earth,” Int. Appl. Mech., 50, No. 6, 721–729 (2014).
Yu. I. Neimark and P. S. Landa, Stochastic and Chaotic Oscillations, Kluwer, Dordrecht (1992).
L. P. Shilnikov, A. L. Shilnikov, D. V. Turaev, and L. O. Chua, Methods of Qualitative Theory in Nonlinear Dynamics, Part I, World Scientific (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 (2001).
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Translated from Prikladnaya Mekhanika, Vol. 51, No. 2, pp. 122–132, March–April 2015.
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Martynyuk, A.A., Nikitina, N.V. Bifurcations and Multistability of the Oscillations of a Three-Dimensional System. Int Appl Mech 51, 223–232 (2015). https://doi.org/10.1007/s10778-015-0687-5
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DOI: https://doi.org/10.1007/s10778-015-0687-5