We present an algorithm for reconstructing the bifurcation structure of a dynamical
system from time series. The method consists in finding a parameterized predictor
function whose bifurcation structure is similar to that of the given system. Nonlinear
autoregressive (NAR) models with polynomial terms are employed as predictor functions.
The appropriate terms in the NAR models are obtained using a fast orthogonal search
scheme. This scheme eliminates the problem of multiparameter optimization and makes
the approach robust to noise. The algorithm is applied to the reconstruction of the
bifurcation diagram (BD) of a neuron model from the simulated membrane potential waveforms.
The reconstructed BD captures the different behaviors of the given system. Moreover,
the algorithm also works well even for a limited number of time series.
Keywords:
Bifurcation Diagram Reconstruction - Time Series Analysis - Nonlinear Autoregressive
Models
