Abstract
We investigate numerically the dynamics of both symmetric and asymmetric Van der Pol-Duffing oscillators driven by a periodic force F(t) = f cosωt. Each system is modeled by a different second order nonautonomous nonlinear ordinary differential equation controlled by five parameters. Our investigation takes into account the (ω, f) parameter-space in the two systems, keeping the other three parameters fixed. We verify the existence of parameter regions for which the corresponding trajectories in the phase-space are periodic, quasiperiodic, and chaotic, for the symmetric case. In the asymmetric case we verify the existence only of periodic and chaotic regions in the (ω, f) parameter-space. Finally, we also investigate the organization of the dynamics in the two systems, identifying Fibonacci and period-adding sequences of periodic structures.
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References
J. Cui, J. Liang, Z. Lin, Phys. Scr. 91, 015201 (2016)
V. Wiggers, P.C. Rech, Chaos Soliton Fract. 103, 632 (2017)
A.J. Brizard, M.C. Westland, Commun. Nonlinear Sci. Numer. Simulat. 43, 351 (2017)
C. Li, W. Xu, L. Wang, D.X. Li, Chin. Phys. B 22, 110205 (2013)
Y.H. Kao, C.S. Wang, Phys. Rev. E 48, 2514 (1993)
P. Ghorbaniana, S. Ramakrishnana, A. Whitmanb, H. Ashrafiuona, Biomed. Signal Process. Control 15, 1 (2015)
A. Kumar, P. Mohanty, Sci. Rep. 7, 411 (2017)
H.G. Schuster, W. Just, Deterministic Chaos an introduction (Wiley-VCH, Weinheim, 2005)
H.A. Albuquerque, R.M. Rubinger, P.C. Rech, Phys. Lett. A 372, 4793 (2008)
C. Bonatto, J.A.C. Gallas, Phys. Rev. E 75, 055204 (2007)
T.S. Krüger, P.C. Rech, Eur. Phys. J. D 66, 12 (2012)
F.G. Prants, P.C. Rech, Eur. Phys. J. B 87, 196 (2014)
P.C. Rech, Int. J. Bifurc. Chaos 25, 1530035 (2015)
P.C. Rech, Phys. Scr. 91, 075201 (2016)
S.L.T. de Souza, A.M. Batista, M.S. Baptista, I.L. Caldas, J.M. Balthazar, Physica A 466, 224 (2017)
P.C. Rech, Phys. Scr. 92, 045201 (2017)
P.C. Rech, Eur. Phys. J. B 90, 251 (2017)
M. Borghezan, P.C. Rech, Chaos Soliton Fract. 97, 15 (2017)
V. Wiggers, P.C. Rech, Int. J. Bifurc. Chaos 27, 1730023 (2017)
A.C. Mathias, P.C. Rech, Neural Networks 34, 42 (2012)
P.C. Rech, Eur. Phys. J. B 86, 356 (2013)
R.A. Dunlap, The golden ratio and Fibonacci numbers (World Scientific, Singapore, 2003)
J.A.C. Gallas, Phys. Rev. Lett. 70, 2714 (1993)
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Wiggers, V., Rech, P.C. On symmetric and asymmetric Van der Pol-Duffing oscillators. Eur. Phys. J. B 91, 144 (2018). https://doi.org/10.1140/epjb/e2018-90295-1
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DOI: https://doi.org/10.1140/epjb/e2018-90295-1