Abstract
This paper studies the oscillatory behavior for a coupled van der Pol-Duffing oscillator with delay. Two theorems are provided to guarantee the oscillation of the system. Computer simulations are given to support the theoretical analysis.
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References
Li, X.Y., Ji, J.C., Hansen, C.H.: Dynamics of two delay coupled van Der Pol oscillators. Mech. Res. Commun. 33, 614–627 (2006)
Zhang, J.M., Gu, X.S.: Stability and bifurcation analysis in the delay-coupled van Der Pol oscillators. Appl. Math. Model. 34, 2291–2299 (2010)
Sabarathinam, S., Thamilmaran, K., Borkowski, L., Perlikowski, P., Bzeski, P., Stefanski, A., Kapitaniak, T.: Transient chaos in two coupled, dissipatively perturbed Hamiltonian duffing oscillators. Commun. Nonlinear. Sci. Numer. Simul. 18, 3098–3107 (2013)
Kuznetsov, A.P., Stankevich, N.V., Turukina, L.V.: Coupled van der Pol-Duffing oscillators: phase dynamics and structure of synchronization tongues. Physica D 238, 1203–1215 (2009)
Kuznetsov, A.P., Paksyutov, V.I.: Feature of the parameter space structure of two non -identical coupled van der Pol-Duffing oscillators. Appl. Nonlin. Dynam. 13, 3–19 (2005)
Peano, V., Thorwart, M.: Dynamics of the quantum duffing oscillator in the driving induced bistable regime. Chem. Phys. 322, 135–143 (2006)
Camacho, E., Rand, R.H., Howland, H.: Dynamics of two van der Pol oscillators coupled via a bath. Int. Solids Struct. 41, 2133–2143 (2004)
Kuznetsov, A.P., Paksyutov, V.I., Roman, Y.P.: Features of the synchronization of coupled van der Pol oscillators with nonidentical control parameters. Tech. Phys. Lett. 8, 636–638 (2007)
Gendelman, O.V., Starosvetsky, Y.: Quasiperiodic response regimes of linear oscillator coupled to nonlinear energy sink under periodic forcing. Trans. ASME J. Appl. Mech. 74, 325–331 (2007)
Rusinek, R., Weremczuk, A., Kecik, K., Warminski, J.: Dynamics of a time delayed Duffing oscillator. Int. J. Nonlin. Mech. 65, 98–106 (2014)
Siewe Siewe, M., Tchawoua, C., Rajasekar, S.: Parametric resonance in the Rayleigh-Duffing oscillator with time-delayed feedback. Commun. Nonlinear Sci. Num. Simul. 17, 4485–4493 (2012)
Beregov, R.Y., Melkikh, A.V.: De-synchronization and chaos in two inductively coupled Van der Pol auto-generators. Chaos Solitons Fractals 73, 17–28 (2015)
Sun, Y., Xu, J.: Experiments and analysis for a controlled mechanical absorber considering delay effect. J. Sound Vibr. 339, 25–37 (2015)
Zhang, C.M., Li, W.X., Wang, K.: Boundedness for network of stochastic coupled van Der Pol oscillators with time-varying delayed coupling. Appl. Math. Model. 37, 5394–5402 (2013)
Horn, R.A., Johnso, C.R.: Matrix Analysis. Cambridge Press, Cambridge (1990)
Acknowledgements
This research was supported by NNSF of China (11361010), the high school specialty and curriculum integration project of Guangxi Zhuang Autonomous Region (GXTSZY2220), the SRF of the Education Department of Guangxi Province (LX2014330), and the Key Discipline of Statistics of Hechi University of China (20133).
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Lin, Y., Hou, Z. (2015). Oscillatory Behavior of the Solutions for a Coupled van der Pol-Duffing Oscillator with Delay. In: Huang, DS., Jo, KH., Hussain, A. (eds) Intelligent Computing Theories and Methodologies. ICIC 2015. Lecture Notes in Computer Science(), vol 9226. Springer, Cham. https://doi.org/10.1007/978-3-319-22186-1_47
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DOI: https://doi.org/10.1007/978-3-319-22186-1_47
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