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

This paper presents an analysis of the dynamical behaviour of a non-symmetric oscillator with piecewise-linearily. 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, Poincare 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. (C) 2001 Elsevier Science Ltd. All rights reserved.