Experimental control of chaos in a delayed high-dimensional system

We introduce a novel control method for a delayed dynamical system exhibiting high-dimensional chaos. The control is based on a negative feedback loop with an adaptive filtering, consisting of a selective filter, centered at the frequency of the orbit to be stabilized, with the addition of a time derivative correction. The validity of the method is also discussed in the framework of a space-like representation adopted to study the analogies between delayed dynamical systems and spatially extended systems. PACS. 05.45.-a Nonlinear dynamics and nonlinear dynamical systems – 42.50.Lc Quantum fluctuations, quantum noise, and quantum jumps – 42.55.Lt Gas lasers including excimer and metal-vapor lasers