Andronov-Hopf bifurcation of sinusoidal oscillators under the influence of noise

We consider Andronov Hopf bifurcation in sinusoidal electrical oscillators under noisy disturbance. For this purpose the deterministic description of oscillators must be generalized using the concept of so-called invariant measures. It turns out that in noisy oscillators two inequivalent bifurcation approaches are available. By means of the van der Pol oscillator these noisy Andronov Hopf bifurcation concepts are illustrated.