Reconstructing bifurcation diagrams of dynamical systems using measured time series

We present an algorithm for reconstructing the bifurcation structure of a d ynamical system from time series. The method consists in finding a paramete rized predictor function whose bifurcation structure is similar to that of the given system, Nonlinear autoregressive (NAR) models with polynomial ter ms are employed as predictor functions. The appropriate terms in the NAR mo dels are obtained using a fast orthogonal search scheme. This scheme elimin ates the problem of multiparameter optimization and makes the approach robu st to noise. The algorithm is applied to the reconstruction of the bifurcat ion diagram (BD) of a neuron model from the simulated membrane potential wa veforms. The reconstructed ED captures the different behaviors of the given system. Moreover, the algorithm also works well even for a limited number of time series.