STOCHASTIC TRACKING IN NONLINEAR DYNAMICAL-SYSTEMS

In a previous paper [Phys. Rev. A 46, 7439 (1992)] we have introduced an alternative continuation method which does not require an analytica l model, but only an experimental time series. Using a predictor-corre ctor technique, the method tracks a given unstable orbit through diffe rent bifurcation regimes by varying an accessible system parameter. In this method, the continuation parameter was varied deterministically. That is, the location of the parameter is chosen by the experimenter. In this paper we introduce a similar algorithm, but now the parameter is varied randomly. A correction procedure is introduced so that cont rol of an unstable orbit is not lost as the parameter changes. Moreove r, we show that the small-amplitude feedback-control technique used fo r correction allows large-amplitude bursts in the parameter. These fea tures are useful to experimentalists for canceling drift in experiment s, which is inevitable at some level.