Generalized one-parameter bifurcation diagram reconstruction using time series. (English) Zbl 0988.37095

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.


37M10 Time series analysis of dynamical systems
37G99 Local and nonlocal bifurcation theory for dynamical systems
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