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Chaotic breathers in delayed electro-optical systems

Chembo Kouomou, Yanne; Colet, Pere; Larger, Laurent; Gastaud, Nicolas
Physical Review Letters 95, 203903 (1-4) (2005)

We show that in integro-differential delayed dynamical systems, a hybrid state of simultaneous fastscale 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.