Bifurcations in noisy nonlinear networks and systems

In this paper, we discuss the analysis of noisy nonlinear systems and circuits. Especially we consider circuits with an oscillatory behavior and limit cycles, respectively. Moreover, we study the 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 probability functions as well as invariant measures. It turns out that these two bifurcation approaches are not equivalent in general. We illustrate these noisy bifurcation concepts by means of a Meissner oscillator including a transistor.