Tracking unstable orbits in experiments

Abstract

We present an alternative continuation method for tracking unstable periodic orbits by slowly varying an available system parameter. This is a predictor-corrector method for which we assume that initially the orbit is on a chaotic attractor. As we vary the parameter, the method can be used to track the orbit through regimes not necessarily chaotic. The method is designed for experimental situations in which we have no analytical knowledge of the system dynamics and only an experimental time series of the variables involved is available. We present numerical results of the method using the Hénon map.