The response of dimensionless mechanical systems containing fractional orders excited by color noise is studied.Firstly,based on the mechanical system containing fractional order,the color noise is introduced and differential approximate transformation of the fractional order defined by Caputo is performed using the Gamma function and its properties.Secondly,the stochastic averaging method is borrowed to reduce the dimensionality of the system,so that the FPK equation of the control system response is obtained.Finally,the effect of color noise on the response of the fractional order mechanical system is analyzed based on the smooth solution of the FPK equation.The results show that the probability of the system reaching stability increases at fractional order,while the increase of the noise intensity D and the correlation time τ makes the probability of the system reaching stability decrease,and in addition the increase of the noise intensity D and the correlation time τ induces the stochastic P-branching.
关键词
色噪声/分数阶近似/随机平均法/随机P分岔
Key words
color noise/fractional order approximation/stochastic averaging/stochastic P-branching
维普
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