Stability and Hopf bifurcation of a Nonlinear oscillator with multiple time-delays |
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| Authors: | Raghavendra D Naik Pravin M Singru |
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| Institution: | 1. Department of Civil Engineering, University of Guilan, Rasht, Iran;2. Department of Civil Engineering, Sharif University of Technology, Tehran, Iran;1. Department of Mathematics, Shanghai University, Shanghai 200444, PR China;2. School of Mathematics and Physics, Changzhou University, Changzhou 213016, Jiangsu, PR China;1. Centre for Quantum Software and Information, University of Technology Sydney, Australia;2. State Key Laboratory of Computer Science, ISCAS, Beijing, China;3. University of Chinese Academy of Sciences, Beijing, China;1. Laboratoire d’Analyse Numérique et d’Informatique, Université Gaston Berger, B.P. 234, Saint-Louis, Sénégal;2. Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla, Spain |
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| 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. |
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