Time-Delayed Feedback Control Method for Dynamical Symmetry Breaking in a Periodically Driven Bistable System

(Received August 7, 2005) With the aim of formulating a method to control dynamic phase transitions in periodically driven bistable systems with reversal symmetry, a time-delayed feedback control method to stabilize an unstable periodic orbit in the broken symmetric regime is studied. In order to overcome a limitation of the conventional time-delayed feedback method, another extended scheme is proposed, and its improved ability with respect to stabilization is proved. Through the linear stability analysis of model controlled systems driven by sinusoidal fields, basic differences between the conventional and proposed methods are extracted. It is clarified that a few characteristics around the bifurcation point from the pitchfork critical branch to the Hopf branch and the turning point of the Hopf critical branch classify essential features of the stability diagram and concern restrictions for stabilization. Within the linear stability treatment, this paper estimates a safe choice and an effective range of feedback gains in the proposed method.