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Stability and Hopf bifurcation of a Nonlinear oscillator with multiple time-delays

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  • Naik, Raghavendra D.
  • Singru, Pravin M.

Abstract

This paper examines dynamical behavior of a nonlinear oscillator which models a quarter-car forced by the road profile. The effect of multiple time delays is studied in detail. The focus is on the influence of delay in the system. This naturally gives rise to a delay differential equation (DDE) model of the system. The domain where the control is efficient in reducing the amplitude of vibration is found by the harmonic balance method. Technical stability within definite time and asymptotic stability is derived for selected gain control parameters. The control gain parameters are chosen according to technical and asymptotic stability. The energy analysis is a combination of Lyapunov’s function and the averaging technique, and is used to analyze the Hopf bifurcation.

Suggested Citation

  • Naik, Raghavendra D. & Singru, Pravin M., 2012. "Stability and Hopf bifurcation of a Nonlinear oscillator with multiple time-delays," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1387-1396.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:11:p:1387-1396
    DOI: 10.1016/j.chaos.2012.06.006
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    References listed on IDEAS

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    1. Hu, H.Y. & Wang, Z.H., 2009. "Singular perturbation methods for nonlinear dynamic systems with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 13-27.
    2. Sun, Zhongkui & Xu, Wei & Yang, Xiaoli & Fang, Tong, 2006. "Inducing or suppressing chaos in a double-well Duffing oscillator by time delay feedback," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 705-714.
    3. Ji, J.C. & Zhang, N. & Gao, Wei, 2009. "Difference resonances in a controlled van der Pol-Duffing oscillator involving time delay," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 975-980.
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