Abstract:
We consider a system of two coupled Van der Pol-Duffing oscillators with Huygens coupling as an appropriate model of two mechanical oscillators connected to a movable platform via a spring. We examine the complicated dynamics of the system and study its multistable behavior. In particular, we reveal the co-existence of several chaotic regimes and study the structure of the associated riddled basins.
Keywords:
Van der Pol–Duffing oscillator, coupled systems, chaotic oscillations.
Citation:
V. N. Belykh, E. V. Pankratova, “Chaotic dynamics of two Van der Pol–Duffing oscillators with Huygens coupling”, Regul. Chaotic Dyn., 15:2-3 (2010), 274–284
\Bibitem{BelPan10}
\by V. N. Belykh, E. V. Pankratova
\paper Chaotic dynamics of two Van der Pol–Duffing oscillators with Huygens coupling
\jour Regul. Chaotic Dyn.
\yr 2010
\vol 15
\issue 2-3
\pages 274--284
\mathnet{http://mi.mathnet.ru/rcd494}
\crossref{https://doi.org/10.1134/S1560354710020140}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2644336}
\zmath{https://zbmath.org/?q=an:1203.37054}
Linking options:
https://www.mathnet.ru/eng/rcd494
https://www.mathnet.ru/eng/rcd/v15/i2/p274
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Liang-qiang Zhou, Fang-qi Chen, “Chaotic Motions of the van der Pol-Duffing Oscillator Subjected to Periodic External and Parametric Excitations with Delayed Feedbacks”, Acta Math. Appl. Sin. Engl. Ser., 40:4 (2024), 1111
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Mao X., Lei F., Li X., Ding W., Shi T., “Multiple Bifurcations and Complex Responses of Nonlinear Time-Delay Oscillators”, J. Comput. Nonlinear Dyn., 16:11 (2021), 111001
D. A. Grechko, N. V. Barabash, V. N. Belykh, “Homoclinic Orbits and Chaos in Nonlinear Dynamical Systems: Auxiliary Systems Method”, Lobachevskii J Math, 42:14 (2021), 3365
G K Annakulova, “Orbital stability analysis of trajectories of highly nonlinear dynamic systems with feedback coupling”, J. Phys.: Conf. Ser., 2131:3 (2021), 032038
Pena Ramirez J., Nijmeijer H., “Enforcing Synchronization in Oscillators With Huygens' Coupling Via Feed-Forward Control”, Nonlinear Dyn., 98:4, SI (2019), 3009–3023
Siewe M.S., Kenfack W.F., Kofane T.C., “Probabilistic Response of An Electromagnetic Transducer With Nonlinear Magnetic Coupling Under Bounded Noise Excitation”, Chaos Solitons Fractals, 124 (2019), 26–35
Allan R. Willms, Petko M. Kitanov, William F. Langford, “Huygens' clocks revisited”, R. Soc. open sci., 4:9 (2017), 170777
Jonatan Pena Ramirez, Ricardo Cuesta Garcia, Joaquin Alvarez, 2016 Australian Control Conference (AuCC), 2016, 87
Hong Zang, Tonghua Zhang, Yanduo Zhang, “Stability and bifurcation analysis of delay coupled Van der Pol–Duffing oscillators”, Nonlinear Dyn, 75:1-2 (2014), 35
P. M. Kitanov, W. Langford, A. R. Willms, “Double Hopf Bifurcation with Huygens Symmetry”, SIAM J. Appl. Dyn. Syst., 12:1 (2013), 126
Hiba Sheheitli, Richard H. Rand, “Dynamics of a mass–spring–pendulum system with vastly different frequencies”, Nonlinear Dyn, 70:1 (2012), 25
E.V. Pankratova, V.N. Belykh, “Synchronization of self-sustained oscillators inertially coupled through common damped system”, Physics Letters A, 376:45 (2012), 3076
R. E. Kondrashov, A. D. Morozov, “O globalnom povedenii reshenii sistemy dvukh uravnenii Dyuffinga – Van der Polya”, Nelineinaya dinam., 7:3 (2011), 437–449
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