Generalized one-parameter bifurcation diagram reconstruction using time series
type: Item
instance of: scholarly article
title: Generalized one-parameter bifurcation diagram reconstruction using time series
zbMATH Open document ID: 0988.37095
DOI: 10.1016/S0167-2789(98)00200-0
author: Yanyan Li
published in: Physica D
publication date: 2002-07-14T00:00:00Z
review text: The authors use time series in reconstructing bifurcation diagrams of dynamical systems that cannot be modeled directly from first principles. Here, at different unknown parameter values time series are available. They are used to obtain a suitable family of nonlinear predictor functions with qualitatively similar bifurcation structure as the original system. The authors propose a generalized one-parameter algorithm in reconstructing the bifurcation diagrams based on principal curves. The bifurcation diagrams of the FritzHugh-Nagumo equations and the Lorenz equations are used for numerical illustration. Important features of the bifurcation diagrams of the original systems, e.g. Hopf bifurcation, are preserved by the reconstruction algorithm.
Mathematics Subject Classification ID: 37M10
Mathematics Subject Classification ID: 37G99
zbMATH DE Number: 1370272
zbMATH Keywords: time series
zbMATH Keywords: bifurcation diagrams
zbMATH Keywords: nonlinear predictor functions
zbMATH Keywords: principal curves
zbMATH Keywords: FritzHugh-Nagumo equations
zbMATH Keywords: Lorenz equations
zbMATH Keywords: Hopf bifurcation
MaRDI profile type: Publication
cites work: The role of the likelihood function in the estimating of chaos models
cites work: Nonlinear prediction of chaotic time series
cites work: Recognizing chaotic time-waveforms in terms of a parametrized family of nonlinear predictors
cites work: Reconstructing bifurcation diagrams only from time-waveforms
cites work: Q3658782
cites work: Q3805940
cites work: Multilayer feedforward networks are universal approximators
cites work: Principal Curves
cites work: Q5287558
cites work: Q4692840
cites work: Deterministic Nonperiodic Flow
cites work: The Lorenz equations: bifurcations, chaos, and strange attractors
cites work: Q3745059
cites work: Robust Locally Weighted Regression and Smoothing Scatterplots
full work available at URL: s0167-2789(98)00200-0
OpenAlex ID: W2076123670
Wikidata QID: Q126572519
description: scientific article; zbMATH DE number 1370272