Abstract

In this work we present an efficient method to control a delayed feedback system These systems, for delays long with respect to the intrinsic decorrelation time corresponding to a short-delay dynamics, display a high dimension chaotic behavior. A suitable space-like representation provides an analogy between delayed systems and space extended systems The analogy rests on the fact that the time variable t can be decomposed into a continuous spacelike variable σ (0 ⪯ σ ⪯ τ) and a discrete timelike variable nτ t = σ + nτ where τ is the delay time In this framework, the long-range temporal interaction due to the delayed feedback can be considered as a local interaction from one to the next delay unit Thus, the behavior of such a system can be studied by representing the original signal x(t) as a space-time plot of a one-dimensional spatial system of length L=τ on a discrete-time lattice Typically, when the delay τ is larger than the characteristic oscillating period, it is possible to observe phase defects, i e points where the phase presents a discontinuity and the amplitude goes to zero

© 2000 IEEE