Control of time-delayed feedback systems with application to optics†

Abstract

We have investigated a new control scheme of chaotic orbit for time-delayed feedback systems and have applied this method to an optical system in which the nonlinear function is the so-called ‘Ikeda function”. Discrete time evolution characterizes the delay-differential equation modelling the system for a large enough delay. We use this discrete map to design the control process and we show that stabilized orbits are closed to stable orbits of the original system; moreover, the control signal is built upon real-time trajectories out of the chaotic's system evolution. Analytical predictions are in good agreement with simulations and the experimental results are obtained.

Notes

†A shorter form of this paper was presented at the 1994 Workshop on the Nonlinear Dynamics of Electronic Systems (NDES'94) held at the University of Mining and Metallurgy, Krakow, Poland, on 29-30 July.