Probabilistic distribution and stochastic <i>P</i> -bifurcation of a nonlinear energy-regenerative suspension system with time-delayed feedback control

Abstract Energy-regenerative suspension combined with piezoelectric and electromagnetic transduction has evolved into a core technological pathway in advancing automotive design paradigms. With the aim of improving energy harvesting performance, time-delayed feedback control is widely used in an energy-regenerative suspension system under different external disturbances in this paper. Meanwhile, limited research has addressed the stochastic dynamics of time-delayed nonlinear energy-regenerative suspension systems. Different from previous studies, this work studies the stochastic response and P -bifurcation of the nonlinear energy-regenerative suspension system with time-delayed feedback control. Firstly, an approximately equivalent dimension reduction system is established by the variable transformation method, and then the stationary probability density function of amplitude is obtained by the stochastic averaging method. Secondly, the precision of the method used in this work is verified by comparing the numerical solutions with the analytical results. Finally, based on the stationary probability density function, the influence of system parameters on stochastic P -bifurcation and the mean output power is discussed.