Study On The Onset Condition And Transient Behaviors Of Noise-Induced Bifurcation
To efficiently determine critical condition of noise-induced bifurcation in nonlinear dynamical systems, a stochastic sensitivity function (SSF) around a deterministic periodic attractor is approximated based on stroboscopic mapping. In this way, the confidence ellipses are constructed to judge critical noise intensity
of noise-induced transition phenomena. To effectively capture the larger stochastic transient behaviors after the critical condition, 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 two proposed methods is demonstrated through the study of a pendulum system under external periodic excitation and additive noise.
CYBERNETICS AND PHYSICS, Vol. 4, No. 4. 2015, 105-111.