Noise-induced fluctuations of period lengths of stable periodic orbits.

We discuss a class of one-dimensional maps, which possesses a globally attracting stable periodic orbit. Despite a strongly negative Lyapunov exponent, a small amount of noise can introduce fluctuations of the period length. It is shown that this is a reasonable model for the observed dynamics of a bubble formation experiment in a heated capillary embedded in boiling water.

Markov models from data by simple nonlinear time series predictors in delay embedding spaces.

We analyze prediction schemes for stochastic time series data. We propose that under certain conditions, a scalar time series, obtained from a vector-valued Markov process can be modeled as a finite memory Markov process in the observable. The transition rules of the process are easily computed using simple nonlinear time series predictors originally proposed for deterministic chaotic signals.