Abstract
Response and bifurcation of fractional Duffing oscillator under recycling noise and time-delayed feedback control are investi-gated.Firstly,based on the principle of the minimum mean square error and small time-delayed approximation and linearize the cubic stiff-ness term,the fractional derivative is equivalent to a linear combination of damping and restoring forces,and the original system is simpli-fied into an equivalent integer order system.Secondly,the Ito differential equations and one-dimensional Markov process are obtained ac-cording to stochastic averaging method,and the stochastic stability and stochastic bifurcation of the system are analyzed.Lastly,through joint probability density function diagram and the stationary probability density function diagram,the stochastic bifurcation behavior of system under the different time-delay,fractional order and noise intensity are discussed respectively,the validity of the theory and the oc-currence of bifurcation phenomenon are verified.
基金项目
国家自然科学基金(61863022)
Key Project of Gansu Province Natural Science Foundation(23JRRA882)
NETL
NSTL
万方数据