Stochastic Sensitivity Analysis of Noise-Induced Oscillations in Adler Model.

We consider Adler model with the saddle-node bifurcation on the invariant circle. Near this bifurcation, even weak random disturbances can generate noise-induced spike oscillations. Corresponding random phase trajectories form stochastic bundle. A dispersion of random trajectories in this bundle is non-uniform. To approximate this dispersion, we propose a new constructive approach based on the stochastic sensitivity analysis and method of ”freezing” of the phase variable. A mathematical description of this approach is given. An extension of this theory for complex systems with so-called sequential dynamics is discussed. [ABSTRACT FROM AUTHOR]