Location of Repository

Analysis of period-doubling and chaos of a non-symmetric oscillator with piecewise-linearity

By Q. Cao, L. Xu, K. Djidjeli, W.G. Price and E.H. Twizell

Abstract

This paper presents an analysis of the dynamical behaviour of a non-symmetric oscillator with piecewise-linearity. The Chen–Langford (C–L) method is used to obtain the averaged system of the oscillator. Using this method, the local bifurcation and the stability of the steady-state solutions are studied. A Runge–Kutta method, Poincaré map and the largest Lyapunov’s exponent are used to detect the complex dynamical phenomena of the system. It is found that the system with piecewise-linearity exhibits periodic oscillations, period-doubling, period-3 solution and then chaos. When chaos is found, it is detected by examining the phase plane, bifurcation diagram and the largest Lyapunov’s exponent. The results obtained in this paper show that the vibration system with piecewise-linearity do exhibit quite similar dynamical behaviour to the discrete system given by the logistic map

Topics: TK, TA, QC
Year: 2001
OAI identifier: oai:eprints.soton.ac.uk:22789
Provided by: e-Prints Soton

Suggested articles

Preview


To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.