Super and sub-critical Hopf bifurcation leading to chaos: theory and experiments

Summary form only given. One of the simplest optical system exhibiting chaotic dynamics is Ikeda's problem modeling a passive cavity subject to optical or optoelectronic feedback. But more recently, a variety of new optoelectronic chaos generators using a delayed feedback have been developed. As Ikeda's system, these systems are accurately described by first order delay differential equations. The first dynamical instability corresponds to a Hopf bifurcation leading to time-periodic oscillations. If the bifurcation is super-critical, a smooth transition to oscillations is observed as the control parameter passes the Hopf bifurcation point. On the other hand, if the bifurcation is sub-critical, a hard transition to large amplitude oscillations can be expected.