Control of defects and spacelike structures in delayed dynamical systems

Abstract

In many nonequilibrium dynamical situations delays are crucial in inducing chaotic scenarios. In particular, a delayed feedback in an oscillator can break the regular oscillation into trains mutually uncorrelated in phase, whereby the phase jumps are localized as defects in an extended system. We show that an adaptive control procedure is effective in suppressing these defects and stabilizing the regular oscillations. The analysis of the transient times for achieving control demonstrates that stabilization is obtained within an amplitude turbulent regime, analogous to what is present in spatially distributed systems. The control technique is robust against the presence of large amounts of noise.