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

作者：Cao Q; Xu L; Djidjeli K^*; Price WG; Twizell EH

来源：Chaos Solitons & Fractals, 2001, 12(10): 1917-1927.

DOI：10.1016/S0960-0779(00)00155-7

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.

• 出版日期2001-8
• 单位山东理工大学