Reconstructing bifurcation diagrams from noisy time series using nonlinear autoregressive models

Epifanio Bagarinao; Khashayar Pakdaman; Taishin Nomura; Shunsuke Sato

doi:10.1103/physreve.60.1073

Abstract

We introduce a formalism for the reconstruction of bifurcation diagrams from noisy time series. The method consists in finding a parametrized predictor function whose bifurcation structure is similar to that of the given system. The reconstruction algorithm is composed of two stages: model selection and bifurcation parameter identification. In the first stage, an appropriate model that best represents all the given time series is selected. A nonlinear 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.

Keywords

Autoregressive modelBifurcation diagramBifurcationSeries (stratigraphy)Nonlinear systemApplied mathematicsTime seriesBifurcation theoryMathematicsNonlinear autoregressive exogenous modelComputer sciencePhysicsStatistics

Affiliated Institutions

The University of Osaka JP

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Publication Info

Year: 1999
Type: article
Volume: 60
Issue: 1
Pages: 1073-1076
Citations: 31
Access: Closed

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APA Style

                            
                                
                                    Epifanio Bagarinao, 
                                
                                    Khashayar Pakdaman, 
                                
                                    Taishin Nomura
                                
                                et al.
                            
                            (1999). 
                            Reconstructing bifurcation diagrams from noisy time series using nonlinear autoregressive models. 
                            Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
                            , 60
                            (1)
                            , 1073-1076.
                            https://doi.org/10.1103/physreve.60.1073
                        

Identifiers

DOI: 10.1103/physreve.60.1073