The effects of stochastic excitation on the period-doubling bifurcation and chaotic motions of the softening Duffing oscillator, are discussed in detail. 摘要討論了有界雜訊激勵對軟彈簧杜芬振子的倍周期分岔至混沌運動的影響。
Neimark-R.J.Sacker bifurcation and period-doubling bifurcation existed under certain parameters, which will evolve to chaos and hyperchaos with the variation of the parameters. 研究發現系統在一定參數條件下存在內衣馬克一沙克分岔和倍周期分岔，隨著參數的變化系統演化為混沌和超混沌。
