SELECTIVE STABILIZATION OF VERY LONG UNSTABLE PERIODIC-ORBITS IN CHAOTIC SYSTEMS

We propose a novel extension of Pyragas' method to stabilise arbitrari ly long unstable periodic orbits (UPOs) in chaotic systems. No restric tions are imposed on the dimensionality of the chaotic attractor and t he system is sampled using time series of a single scalar variable. Wa ys to estimate all of the necessary control parameters are presented. The method is tested stabilising UPOs in the Mackey-Glass system that has an infinite dimensional state space due to an inherent time delay. The effective attractor dimension can be tuned to any convenient valu e by changing the delay, which allows one to test for effects of high dimensional chaos. (C) 1997 Elsevier Science B.V.