Volume 13 Number 3 (Mar. 2018)
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JCP 2018 Vol.13(3): 271-278 ISSN: 1796-203X
doi: 10.17706/jcp.13.3.271-278

A Quantitative Method for Evaluating Reconstructed One-Dimensional Bifurcation Diagrams

Yoshitaka Itoh, Masaharu Adachi
Department of Electrical and Electronic Engineering, Tokyo Denki University, 5 Senju-Asachicho Adachi-ku, Tokyo , Japan.
Abstract—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.

Index Terms—Chaos, reconstruction of bifurcation diagram, time-series prediction, extreme learning machine, evaluation methods, levenshtein distance.

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Cite: Yoshitaka Itoh, Masaharu Adachi, "A Quantitative Method for Evaluating Reconstructed One-Dimensional Bifurcation Diagrams," Journal of Computers vol. 13, no. 3, pp. 271-278, 2018.

General Information

ISSN: 1796-203X
Frequency: Monthly (2006-2014); Bimonthly (Since 2015)
Editor-in-Chief: Prof. Liansheng Tan
Executive Editor: Ms. Cherry L. Chen
Abstracting/ Indexing: DBLP, EBSCO, DOAJ, ProQuest, INSPEC, ULRICH's Periodicals Directory, WorldCat, CNKI,etc
E-mail: jcp@iap.org
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