Predicting Catastrophes in Nonlinear Dynamical Systems by Compressive Sensing

Wen-Xu Wang, Rui Yang, Ying-Cheng Lai, Vassilios Kovanis, and Celso Grebogi
Phys. Rev. Lett. 106, 154101 – Published 15 April 2011

Abstract

An extremely challenging problem of significant interest is to predict catastrophes in advance of their occurrences. We present a general approach to predicting catastrophes in nonlinear dynamical systems under the assumption that the system equations are completely unknown and only time series reflecting the evolution of the dynamical variables of the system are available. Our idea is to expand the vector field or map of the underlying system into a suitable function series and then to use the compressive-sensing technique to accurately estimate the various terms in the expansion. Examples using paradigmatic chaotic systems are provided to demonstrate our idea.

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  • Received 23 November 2010

DOI:https://doi.org/10.1103/PhysRevLett.106.154101

© 2011 American Physical Society

Authors & Affiliations

Wen-Xu Wang1,*, Rui Yang1,†, Ying-Cheng Lai1,2, Vassilios Kovanis3, and Celso Grebogi2

  • 1School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA
  • 2Institute for Complex Systems and Mathematical Biology, King’s College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
  • 3Sensors Directorate, 2241 Avionics Circle, Wright Patterson AFB, Ohio 45433, USA

  • *wenxuw@gmail.com
  • ryang8@asu.edu

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Vol. 106, Iss. 15 — 15 April 2011

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