Detecting unstable periodic orbits in high-dimensional chaotic systems from time series

Reconstruction meeting with adaptation

Huanfei Ma, Wei Lin, Ying-Cheng Lai

Research output: Contribution to journalArticle

7 Citations (Scopus)

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.

Original languageEnglish (US)
Article number050901
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume87
Issue number5
DOIs
StatePublished - May 10 2013

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Orbit
Chaotic System
Periodic Orbits
High-dimensional
Time series
Unstable
orbits
Adaptive Synchronization
Nonlinear Dynamics
Approximation Theory
Glass
synchronism
Neural Networks
glass
approximation

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Medicine(all)

Cite this

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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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