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Predicting bifurcation points via extreme learning machine methods trained on time-series datasets and parameters in discrete dynamical systems

Kaito Kato1,*, Yoshitaka Itoh2, and Takuji Kousaka1

  • *Contact author: k.kato@ieee.org
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Phys. Rev. E 112, 014208 – Published 10 July, 2025

DOI: https://doi.org/10.1103/qzl8-4c4g

Abstract

This paper proposes a data-driven method for obtaining the bifurcation points of a system utilizing a method based on Extreme Learning Machine with input parameter channels (ELM-IPC) trained on the time-series datasets from discrete dynamical systems. The input parameter channels permit the proposed method to align the original parameter spaces of the time-series datasets with the derived parameter spaces of the ELM-IPC model; this results in the accurate analysis of the bifurcation points of a system. To demonstrate the effectiveness of this approach, we apply it to two discrete dynamical systems: the two-dimensional Hénon map and the four-dimensional system comprising two conservatively coupled Hénon maps. Our results indicate that it is possible to obtain the bifurcation points of a system even in parameter spaces where multiple solutions coexist or periodic solutions with periods exceeding 100 are present.

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Phys. Rev. E 112, 014208– Published 10 July, 2025
  • Received 17 December 2024
  • Accepted 17 June 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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