【摘要】 讨论了有界噪声激励对软弹簧杜芬振子的倍周期分岔至混沌运动的影响。利用蒙特卡罗方法,通过对系统受侵蚀安全盆的变化状况进行了观察,并由此对后继动力学分析的初始点进行了选取。系统的相图、倍周期分岔图以及庞加莱映射图等方面的数值结果表明,外加随机激励的作用往往掩盖原确定性系统内在的规则运动,对原确定性系统的运动具有较典型的分散作用,可延缓系统的倍周期分岔,也可使得系统内在随机行为提前发生,即可使得系统更容易出现混沌运动。更多还原

【Abstract】 The effects of stochastic excitation on the period-doubling bifurcation and chaotic motions of the softening Duffing oscillator, are discussed in detail. With Monte-Carlo method, various eroded safe basins of the system are observed, then the reasonable initial value is picked up for the subsequent dynamic analysis. The numerical results from the phase portraits, the period-doubling bifurcation and the Poincare sections show that external stochastic excitation always masks the regular motions of a deterministic system and plays a dissipative role to the motions of the system, which causes the chaotic motions of the system to arise easily, though the period-doubling bifurcation is delayed.更多还原