Control of chaotic spatiotemporal spiking by time-delay autosynchronization

A global time-delayed feedback control is applied to a globally coupled reaction-diffusion system describing charge transport in a bistable semiconductor. We demonstrate that a variety of spatiotemporal unstable periodic orbits (UPOs) embedded in a chaotic attractor of the spatially extended system can be stabilized using an extended time-delay autosynchronization algorithm. These UPOs correspond to spiking current filaments. We critically evaluate analytical approximations for the limits of control originally developed for low-dimensional temporal chaos and show that the delay time can be extrapolated with high accuracy, while the theoretical limit for the control of UPOs in terms of the product of the period and the largest Lyapunov exponent is not reached. If the global feedback is modified by a spatial filter, we achieve stabilization of different spatial patterns. [S1063-651X(99)07911-8].