谐和与宽带噪声联合激励下含分数导数型阻尼的Duffing振子的平稳响应

Stationary response of duffing oscillator with fra ctional derivative damping under combined harmonic and wide band noise xcitations

用广义谐和函数导出了含分数导数型阻尼的Duffing振子在谐和与宽带噪声联合作用下的随机平均方程,然后用有限差分法求解了平均FPK方程得到系统的随机稳态响应,研究了分数阶数对随机跳跃分岔影响。最后,通过与原方程MonteCarlo数字模拟结果的比较,验证了所得结果的正确性。

The averaged It? stochastic differential equations for Duffing oscillator with fractional derivative damping under combined harmonic and wide band noise excitations are obtained by using the generalized harmonic functions. Then, the stationary response is obtained by solving the reduced PFK equation using the finite difference method and the effect of fractional order on the bifurcation of the stochastic jump is investigated. Finally, numerical results are verified by using the results from Monte Carlo simulation of original system.