Summary
International Symposium on Nonlinear Theory and Its Applications
2015
Session Number:B4L-C
Session:
Number:B4L-C-2
Reconstruction of Bifurcation Diagrams with Lyapunov Exponents for Chaotic Systems from Only Time-Series Data
Yoshitaka Itoh, Yuta Tada, Masaharu Adachi,
pp.692-695
Publication Date:2015/12/1
Online ISSN:2188-5079
Summary:
We describe the reconstruction of bifurcation diagrams with Lyapunov exponents for chaotic systems using only data from several time-series. The algorithm, which was originally proposed by Tokunaga et al., for reconstructing a bifurcation diagram with the corresponding Lyapunov exponents is as follows. First, we model a dynamical system of several time-series by a time-series predictor. In this paper, an extreme learning machine is used as the time-series predictor. Next, we estimate the number of significant parameters of the target dynamical system from the modeled dynamical system by principal component analysis. Then, we reconstruct the bifurcation diagrams with the Lyapunov exponents of the target dynamical system. We show the results of numerical experiments on the reconstruction of bifurcation diagrams with Lyapunov exponents for the logistic and Hﾂ'enon maps.