Reconstructing bifurcation diagrams from noisy time series using nonlinearautoregressive models

We introduce a formalism for the reconstruction of bifurcation diagrams fro m noisy time series. The method consists in finding a parametrized predicto r function whose bifurcation structure is similar to that of the given syst em. The reconstruction algorithm is composed of two stages: model selection and bifurcation parameter identification. In the first stage, an appropria te model that best represents all the given time series is selected. A nonl inear autoregressive model with polynomial terms is employed in this study. The identification of the bifurcation parameters from among the many model parameters is done in the second stage. The algorithm works well even for a limited number of time series. [S1063-651X(99)12607-2].