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

Raghavendra D. Naik and Pravin M. Singru

Chaos, Solitons & Fractals, 2012, vol. 45, issue 11, 1387-1396

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:45:y:2012:i:11:p:1387-1396

DOI: 10.1016/j.chaos.2012.06.006

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