Stochastic bifurcation of an asymmetric single-well potential duffing oscillator under bounded noise excitation

The stochastic bifurcation, defined as the collision of a stochastic attractor with a stochastic saddle, of an asymmetric single-well potential Duffing oscillator subject to bounded noise excitation is studied by means of the modified digraph cell mapping method. The vivid evolution of stochastic bifurcation is described in detail. Meanwhile, the invariant manifolds of the system accompanied by the stochastic bifurcation are also obtained by this method. Furthermore, the relationship between unstable manifold and the growth direction in the shape and size of the stochastic attractor and stochastic saddle as the system parameter is varied, is given through our analysis.