Reconstructing One- and Two-Bifurcation Diagrams of All Components in the Rössler Equations Only from Time-Series Data Sets

We reconstruct bifurcation diagrams of all components in the Rossler 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.