Onset Condition And Transient Behaviors Of Noise-Induced Bifurcation
Zigang Li, Kongming Guo, Jun Jiang, Ling Hong
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 and used to judge if the corresponding confidence ellipse is in touch with the manifolds of certain saddle-typed invariant sets in order to obtain the critical noise intensity of noise-induced transition phenomena. Furthermore, to efficiently capture the 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 Duffing oscillator under external periodic excitation and additive noise.