Nonlinear Theory and Its Applications, IEICE
Online ISSN : 2185-4106
ISSN-L : 2185-4106
Special Issue on Recent Progress in Nonlinear Theory and Its Applications
Reconstructing bifurcation diagrams with Lyapunov exponents from only time-series data using an extreme learning machine
Yoshitaka ItohYuta TadaMasaharu Adachi
ジャーナル フリー

2017 年 8 巻 1 号 p. 2-14


We describe a method for reconstructing bifurcation diagrams with Lyapunov exponents for chaotic systems using only time-series data. The reconstruction of bifurcation diagrams is a problem of time-series prediction and predicts oscillatory patterns of time-series data when parameters change. Therefore, we expect the reconstruction of bifurcation diagram could be used for real-world systems that have variable environmental factors, such as temperature, pressure, and concentration. In the conventional method, the accuracy of the reconstruction can be evaluated only qualitatively. In this paper, we estimate Lyapunov exponents for reconstructed bifurcation diagrams so that we can quantitatively evaluate the reconstruction. We also present the results of numerical experiments that confirm that the features of the reconstructed bifurcation diagrams coincide with those of the original ones.

© 2017 The Institute of Electronics, Information and Communication Engineers
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