Stabilizing unstable periodic points of one-dimensional nonlinear systems using delayed-feedback signals.

Abstract

This paper presents a technique which realizes the following operation: a stable orbit in a one-dimensional nonlinear system moves to an already coexisting unstable periodic point and then stabilizes on it. The technique uses two delayed-feedback signals: the first signal destabilizes the nonlinear system such that the orbit wanders about phase space; the second signal stabilizes the wandering orbit onto a desired unstable periodic point. The technique would be useful for experimentalists who want to know the location of the already coexisting unstable point outside chaotic regions. We illustrate the technique using the logistic map. \textcopyright{} 1996 The American Physical Society.