A simple algorithm for testing the stability of periodic solutions of some nonlinear oscillators with large time delay
作者： JunYu Li , Li Zhang , ZaiHua Wang
DOI: 10.1007/S11431-011-4487-9
关键词:
摘要: Periodic solutions occur commonly in linear or nonlinear dynamical systems. In some cases, the stability of a periodic solution holds if rightmost characteristic root has negative real part. Based on Lambert W function, this paper presents simple algorithm for locating oscillators with large time delay. As application, proposed is used to study primary resonance and 1/3 subharmonic Duffing oscillator under harmonic excitation delayed feedback, as well control problem van der Pol by using number case studies. The main advantage that though very implementation, it works effectively high accuracy even delay large.
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Haiyan Hu, Earl H. Dowell, Lawrence N. Virgin, Resonances of a Harmonically Forced Duffing Oscillator with Time Delay State Feedback Nonlinear Dynamics. ,vol. 15, pp. 311- 327 ,(1998) , 10.1023/A:1008278526811
Thomas Erneux, Applied Delay Differential Equations ,(2009)
Chyi Hwang, Yi-Cheng Cheng, A note on the use of the Lambert W function in the stability analysis of time-delay systems Automatica. ,vol. 41, pp. 1979- 1985 ,(2005) , 10.1016/J.AUTOMATICA.2005.05.020
Li Zhang, HuaiLei Wang, HaiYan Hu, Global view of Hopf bifurcations of a van der Pol oscillator with delayed state feedback Science China-technological Sciences. ,vol. 53, pp. 595- 607 ,(2010) , 10.1007/S11431-010-0073-9
L. PALKOVICS, P.J.Th. VENHOVENS, Investigation on Stability and Possible Chaotic Motions in the Controlled Wheel Suspension System Vehicle System Dynamics. ,vol. 21, pp. 269- 296 ,(1992) , 10.1080/00423119208969012
Delay differential equations via the matrix Lambert W function and bifurcation analysis: application to machine tool chatter. Mathematical Biosciences and Engineering. ,vol. 4, pp. 355- 368 ,(2007) , 10.3934/MBE.2007.4.355
Koen Engelborghs, Tatyana Luzyanina, Giovanni Samaey, DDE-BIFTOOL v. 2.00: a Matlab package for bifurcation analysis of delay differential equations TW Reports. pp. 61- 61 ,(2001)
Jian Xu, Kwok Wai Chung, A perturbation-incremental scheme for studying Hopf bifurcation in delayed differential systems Science in China Series E: Technological Sciences. ,vol. 52, pp. 698- 708 ,(2009) , 10.1007/S11431-009-0052-1
Cedric Thieulot, L. P. B. M. Janssen, Pep Español, Smoothed particle hydrodynamics model for phase separating fluid mixtures. I. General equations. Physical Review E. ,vol. 72, pp. 1- 15 ,(2005) , 10.1103/PHYSREVE.72.016713
S. Chatterjee, Vibration control by recursive time-delayed acceleration feedback Journal of Sound and Vibration. ,vol. 317, pp. 67- 90 ,(2008) , 10.1016/J.JSV.2008.03.020