A map-based algorithm for controlling low-dimensional chaos

Abstract

A simple proportional-feedback algorithm for controlling chaos is presented. The scheme is a map-based variation of a method recently proposed by Ott, Grebogi, and Yorke [Phys. Rev. Lett. 64, 1196 (1990)] in which unstable periodic orbits embedded within a strange attractor are stabilized through deliberate perturbations of a system constraint. The simplified method offers advantages for control of systems in which more complicated algorithms might not be feasible due to short time scales or limited computational resources. Applications to chemical and biological models are presented to demonstrate the utility and limitations of the method. Low-dimensional chaos can usually be stabilized through proportional feedback of one parameter; in some cases, however, a linear combination of several parameters must be utilized.