Stochastic response analysis of noisy system with non-negative real-power restoring force by generalized cell mapping method

The stochastic response of a noisy system with non-negative real-power restoring force is investigated. The generalized cell mapping (GCM) method is used to compute the transient and stationary probability density functions (PDFs). Combined with the global properties of the noise-free system, the evolutionary process of the transient PDFs is revealed. The results show that stochastic P-bifurcation occurs when the system parameter varies in the response analysis and the stationary PDF evolves from bimodal to unimodal along the unstable manifold during the bifurcation.