Analysis of stochastic attractors under the stationary point-cycle bifurcation

In this paper, consideration is given to the stationary point-cycle bifurcation in nonlinear dynamical systems affected by random perturbations. To describe probabilistic properties of corresponding stochastic attractors, we propose to use a new construction, i.e., function of stochastic sensitivity. This function allows describing the spread of random trajectories about the determinate attractor in quite a simple manner. The theoretical description of the function of stochastic sensitivity is given both for the stationary point and limit cycle. The potential of this approach is demonstrated by the examples of stochastic Hopf, Van der Pol, and brusselator models.