Master-slave scheme and controlling chaos in the Braiman-Goldhirsch method

Abstract

This Brief Report presents a master-slave scheme to demonstrate explicitly how control chaos works in the Braiman-Goldhirsch method for the one-dimensional map system. The scheme also naturally explains why the anomalous responses arise in a periodically perturbed, unimodal map system. The extension of the masterslave scheme to the D-dimensional map is also presented. ͓S1063-651X͑99͒03404-2͔

Bifurcations Induced by Periodic Forcing and Taming Chaos in Dripping Faucets

“…In the nonfeedback control systems, on the other hand, the applied perturbation is independent of the state of the system. So far, controlling chaos by applying a suitable weak periodic perturbation, which is sometimes called taming chaos, 3) has been studied in a variety of chaotic dynamical systems both theoretically [4][5][6][7] and experimentally. 8) Recently, analyzing a constrained system in which a one-dimensional Poincaré map is derived, Tamura et al 4) showed that taming chaos occurs by a saddle node bifurcation.…”