Dynamic bifurcations: hysteresis, scaling laws and feedback control

We review some properties of dynamical systems with slowly varying parameters, when a parameter is moved through a bifurcation point of the static system. Bifurcations with a single zero eigenvalue may create hysteresis cycles, whose area scales in a nontrivial way with the adiabatic parameter. Hopf bifurcations lead to the delayed appearance of oscillations. Feedback control theory motivates the study of a bifurcation with double zero eigenvalue, in which this delay is suppressed.