A Quantitative Method for Evaluating Reconstructed One-Dimensional Bifurcation Diagrams

We describe a quantitative method for evaluating reconstructed 1-dimensional bifurcation diagrams. We estimate the oscillatory patterns of time-series data by reconstructing the bifurcation diagrams from time-series data alone. Such reconstruction can be used for real-world systems that have variable parameters, such as electric current and power, temperature, pressure, and concentration. In the conventional method, the reconstructed bifurcation diagram is qualitatively compared with the original one. Here, we evaluate the reconstructed 1-dimensional bifurcation diagrams by means of quantitative comparison with the original one. We also present the results of numerical experiments, demonstrating that our method is useful for quantitative evaluation of reconstructed bifurcation diagrams for the Hénon map and the Rössler equations.