Nonlinear dynamics and chaos control for a time delay Duffing system

Abstract

A time delay Duffing system is studied in this paper. This system is forced by harmonically periodic vibration to enrich dynamics behaviors. Because of the nonlinear terms of the system, the system exhibits both regular and chaotic motions. By using Lyapunov direct method, the stability of the controlled system can be determined. And by applying various numerical results, such as phase portraits, Poincare maps, time history and power spectrum analysis, the behaviors of the periodic and chaotic motion are presented. The effects of the change of parameters in the system can be found in the bifurcation diagrams and parametric diagrams. Finally, a time delay feedback controlling method is applied to the system. It is found that the controller can effectively control the chaotic orbits to the regular ones.