Noise-Induced Transitions for Coexisting Periodic Attractors

We consider a dynamical system in the parameter zone admitting two coexisting limit cycles under the transition to chaos via period-doubling bifurcations. Under the random disturbances, noise-induced transitions between two coexisting separate attractors are studied. We suggest a stochastic sensitivity function technique for the
analysis of this type transitions. This approach allows to construct the dispersion ellipses of random trajectories
for any Poincare sections. Possibilities of our descriptive-geometric method for a detailed analysis of noise-induced
transitions between two periodic attractors of Lorenz model are demonstrated.

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