Defects and turbulence in systems with two delays

We introduce a class of systems with multiple, hierarchically long time delays, and using a suitable space-time representation we uncover features otherwise hidden in their temporal dynamics. Erratic behaviour in the case of two delays is shown to ”encode” two-dimensional spiral defects and defects turbulence.
A multiple scale analysis sets the equivalence to a complex Ginzburg-Landau equation.
We also demonstrate this phenomenon for a semiconductor laser with two delayed optical feedbacks.

This is a joint result with G. Giacomelli.