Nonlinear Theory and Its Applications, IEICE
Online ISSN : 2185-4106
ISSN-L : 2185-4106
Special Section on Recent Progress in Nonlinear Theory and Its Applications
Reconstructing one- and two-bifurcation diagrams of all components in the Rössler equations only from time-series data sets
Yoshitaka ItohMasaharu Adachi
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2021 Volume 12 Issue 3 Pages 391-398

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Abstract

We reconstruct bifurcation diagrams of all components in the Rössler equations only from time-series data sets, thereby estimating the attractors when the parameter values are changed. In this study, we show that the bifurcation diagrams of all components can be reconstructed from time-series data of all components. In addition, we estimate the Lyapunov spectrum of the reconstructed bifurcation diagrams. We expect that the reconstruction requires a shorter length of training data when using time-series data sets of all components compared with one component. Accordingly, in numerical experiments, we reconstruct the bifurcation diagrams using training data whose length is shorter than when a bifurcation diagram is reconstructed using training data of one component.

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