FAST-SCALE HYPERCHAOS ON TOP OF SLOW-SCALE PERIODICITY IN DELAYED DYNAMICAL SYSTEMS

We show the coexistence of a fast-scale hyperchaos with a slow-scale periodic behavior in an integro-differential delayed dynamical system. This behavior arises after a sequence of Hopf bifurcations. This new phenomenology is experimentally evidenced with a Mach-Zehnder modulator optically fed by a semiconductor laser, and subjected to a delayed nonlinear electro-optical feedback. A “breathing” dynamics is therefore observed, consisting of ns-timescale hyperchaotic oscillations with a periodic modulation at a μs-timescale. A theoretical understanding of the phenomenon is also provided.