Abstract: The authors analyze the chaotic characters of the Duffing equation coacted on by the periodic stimulating force and bandlimited white noise. Firstly, the critical amplitude value and periodic amplitude value of the system free of noise are detected. Secondly, the phasestate graphs are analyzed with the timecourse curve by keeping the two particular amplitude values while varying the bandlimited noise amplitude values. A thirdly, a similar analysis is done by keeping the amplitude value of bandlimited white noise and varing the amplitude value of the periodic stimulating force. The results show that the system appears chummage state, chaotic state and periodic state in turn as the periodic stimulating force value increasing when the periodic stimulating force is the only input. When the system is in critical state as the bandlimited white noise increases the phasestate graph extends its dynamic range.

Key words: Duffing equation, complicated stimulating force, chaos, phasestate