分数阶Duffing振子的动力学研究

在经典Dtfffing振子中引入分数微分型阻尼项，推导了高效率的数值计算格式，对其表现出来的特有的非线性现象进行讨论．研究表明：分数微分型阻尼的分数阶值较小时，振子将出现倍周期分岔并导致混沌．在不同的外激励频率下，分数微分型Duffing振子会呈现对称性破缺、分岔、混沌等强烈的非线性现象；在一定参数范围内，分数微分型Duffing振子较经典Duffing振子，在较小的激励下即可进入混沌．

Dynamics of fractional duffing oscillator

After introducing fractional damping into classical Duffing oscillator,a high efficient numerical algorithm was deduced.The research on the fractional Duffing oscillator indicates that,decreasing the damping fractional order,the time period of oscillator changes and further goes to chaos.Under the external excitation forces of different frequencies,the strange attractor can be found at a lower frequency.The fractional Duffing oscillator comes into chaotic state earlier than the integral classical Duffing os...