Suppressing Chaos of Duffing-Holmes System Using Random Phase

Li Longsuo

doi:10.1155/2011/538202

Abstract

The effect of random phase for Duffing-Holmes equation is investigated. We show that as the intensity of random noise properly increases the chaotic dynamical behavior will be suppressed by the criterion of top Lyapunov exponent, which is computed based on the Khasminskii's formulation and the extension of Wedig's algorithm for linear stochastic systems. Then, the obtained results are further verified by the Poincaré map analysis, phase plot, and time evolution on dynamical behavior of the system, such as stability, bifurcation, and chaos. Thus excellent agrement between these results is found.

Highlights

For the past ten years, there has been a great deal of interest in the chaos control’s research which has become one of nonlinear scientific field hot spot issues
After OGY methods were proposed by Ott et al 1, various methods for chaos control’s have been given which are composed of the feedback control and the nonfeedback control
Ramesh and Narayanan 10 explored the robustness in nonfeedback chaos control in presence of uniform noise and found that the system would lose control while noise intensity was raised to a threshold level

Summary

Introduction

For the past ten years, there has been a great deal of interest in the chaos control’s research which has become one of nonlinear scientific field hot spot issues. Stochastic forces or random noise have been greatly used in studying the control of chaos. Ramesh and Narayanan explored the robustness in nonfeedback chaos control in presence of uniform noise and found that the system would lose control while noise intensity was raised to a threshold level. Wei and Leng studied the chaotic behavior in Duffing oscillator in presence of white noise by the Lyapunov exponent. To some extent, Duffing system is the basis of lots of complicated dynamics; it has theoretical significance and important actual value. This paper focuses on the study of the influences of random phase on the behaviors of Duffing-Holmes dynamics and shows that the random phase methods can actualize the chaos control. We show that the random phase can control the chaos behaviors by combining the Poincar section and the time history

Chaotic Behavior of Duffing-Holmes System

Suppressing Chaos of the Duffing-Holmes System Using a Random Phase

Conclusions