Coupled generators having the property of multistability (one generator with exponential inertial nonlinearity and Chou generator) are considered. New oscillation conditions occurring under synchronization are established using the characteristic equation for the system of variational equations
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V. S. Anishchenko, Complex Oscillations in Simple Systems [in Russian], Nauka, Moscow (1990).
V. V. Astakhov, A. I. Shabunin, A. N. Sil’chenko, G. I. Strelkova, and V. S. Anishchenko, “Nonlinear dynamics of two Chua generators with capacitive coupling,” Radiotekhn. Elektron., 42, No. 3, 320–327 (1997).
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).
V. S. Anishchenko, V. V. Astakhov, T. E. Vadivasova, O. V. Sosnovtseva, C. W. Wu, and L. Chua, “Dynamics of two coupled Chuas curchuits,” Int. J. Bifurc. Chaos, 5, No. 6, 1677–1699 (1995).
A. I. Khibnik, D. Roose, and L. Chua, Chua’s Circuit: A Paradigm for Chaos, World Scientific, Singapour (1993).
M. Komuro, R. Tokunaga, T. Matsumoto, L. Chua, and A. Hotta, “Global bifurcation analysis of the double-scroll circuit,” Int. J. Bifurc. Chaos, 1, No. 1, 139–182 (2001).
G. A. Leonov, Strange Attractors and Classical Stability Theory, University Press, St. Peterburg (2008).
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, 721–731 (2014).
A. A. Martynyuk and N. V. Nikitina, “Bifurcations and multi-stabilty of the oscillations of a three-dimensional system,” Int. Appl. Mech., 51, No. 2, 223–232 (2015).
A. A. Martynyuk and N. V. Nikitina, “On periodic 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).
L. P. Shilnikov, A. L. Shilnikov, D. V. 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. 2, pp. 110–123, March–April, 2017.
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Martynyuk, A.À., Nikitina, N.V. Bifurcation and Synchronization of Two Coupled Generators. Int Appl Mech 53, 209–219 (2017). https://doi.org/10.1007/s10778-017-0806-6
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DOI: https://doi.org/10.1007/s10778-017-0806-6