复杂策动力项对Duffing方程混沌系统相态的影响

Analysis on the Influence of the Phase-State of Chaotic System in Duffing Equation by Complicated Stimulating Force Item

对经典Duffing方程在周期激励和限带白噪同时作用下的混沌性质进行分析。首先检测出无噪声时系统的临界状态和周期状态的周期激励的幅值,然后分别固定这两个特殊幅值,改变限带白噪的幅值,利用时间历程曲线辅助分析相态图的变化;再固定限带白噪的幅值,改变周期激励的幅值,借助时间历程曲线分析相态图的变化。结果表明:系统只输入周期激励时,随着周期激励幅值的增大,系统依次呈现同宿状态、混沌状态和周期状态;系统处在临界状态时,输入限带白噪声,随着限带白噪声幅值的增大,相态图的轨线运动范围增大。

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 bandlimited 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.