Onset Condition and Transient Behaviors of Noise-induced Bifurcation

To efficiently determine critical condition of noiseinduced bifurcation in nonlinear dynamical systems, a stochastic sensitivity function (SSF) around a deterministic periodic attractor is approximated based on stroboscopic mapping. Then the confidence ellipses are constructed and used to judge if it collides with some invariant sets of system in order to obtain the critical noise intensity of noise-induced transition phenomena. Furthermore, to effectively capture the larger stochastic transient behaviors over the critical noise intensity, an idea of evolving probabilistic vector (EPV) is introduced into the Generalized Cell Mapping method (GCM) in order to enhance the computation efficiency of the numerical method. The feasibility of the proposed methods is demonstrated through the study of a Duffing oscillator under external periodic excitation and additive noise.