<title>Continuous control of chaos by self-controlling feedback: stabilization of unstable periodic and aperiodic orbits</title>

Abstract

Continuous control of chaos by seif-controffing feedback:stabilization of unstable periodic and aperiodic orbitsK. PyragasLehrstuhl Experimentaiphysik II, Universitat Tiibingen, Morgenstelle 14, W-7400 Tubingen, GermanySemiconductor Physics Institute, Gotauto 11, 2600 Vilnius, LithuaniaABSTRACTThe methods of stabilization of unstable periodic and aperiodic orbits of a strange attractor with thehelp of a small time-continuous perturbation are discussed. The perturbation is applied to the system insuch a way that the desired periodic or aperiodic orbits remain unperturbed. An experimental applicationof the methods can be carried out by a purely analogous technique without use of any computer.1. INTRODUCTIONChaotic attractors typically have embedded within them an infinite number of unstable periodicorbits. A few years ago Ott, Grebogi, and Yorke (OGY) employing this key observation suggested ageneral way to control chaos1. A desired periodic motion of an originally chaotic dynamic system canbe achieved through only a small temporal perturbations made in an accessible system parameter. Thisidea has been developed and applied to a variety of dynamical systems, including mechanical, electronic,