Stochastic jump and bifurcation of Duffing oscillator with fractional derivative damping under combined harmonic and white noise excitations

Abstract

The stochastic jump and bifurcation of Duffing oscillator with fractional derivative damping of order α (0< α <1) under combined harmonic and white noise excitations are studied. First, the system state is approximately represented by two-dimensional time-homogeneous diffusive Markov process of amplitude and phase difference using the stochastic averaging method. Then, the method of reduced Fokker–Plank–Kolmogorov (FPK) equation is used to predict the stationary response of the original system. The phenomenon of stochastic jump and bifurcation as the fractional orders' change is examined. ► The stochastic jump and bifurcation as the fractional order change are observed. ► The stochastic jump and bifurcation are explained using the stationary probability density. ► The stochastic jump and bifurcation are examined using the samples of displacement.