We show that in integro-differential delayed dynamical systems, a hybrid state of simultaneous fast-scale chaos and slow-scale periodicity can emerge subsequently to a sequence of Hopf bifurcations. The resulting time trace thereby consists in chaotic oscillations "breathing" periodically at a significantly lower frequency. Experimental evidence of this type of dynamics in delayed dynamical systems is achieved with a Mach-Zehnder modulator optically fed by a semiconductor laser and is subjected to a delayed nonlinear electro-optical feedback. We also propose a theoretical understanding of the phenomenon.

We investigate the detrimental effects of parameter mismatch on the synchronization of semiconductor lasers with electro-optical feedback, whose intensity dynamics can display a hyperchaotic behavior. Analytical techniques are developed to study the statistical properties of the synchronization error as a function of the various types of mismatches. The multiple mismatch case, which is of high experimental interest, is also studied and some compensation conditions allowing the improvement of the synchronization are derived. The analytical predictions are confirmed by numerical simulations and by some experimental measurements.

We analyze the influence of parameter mismatch between emitter and receiver systems on the bit error rate of an optical chaos communication scheme. Intensity hyperchaos is generated in the system by semiconductor lasers with electrooptical feedback. We find analytical predictions for the dependence of the bit error rate with the amplitude of the various mismatches and the statistical properties of the hyperchaotic carrier. A good concordance is found with numerical and experimental results.