Predicting Catastrophes in Nonlinear Dynamical Systems by Compressive Sensing

Wen-Xu Wang, Rui Yang, Ying-Cheng Lai, Vassilios Kovanis, Celso Grebogi

Research output: Contribution to journalArticle

134 Citations (Scopus)

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.

Original languageEnglish
Article number154101
Number of pages4
JournalPhysical Review Letters
Volume106
Issue number15
DOIs
Publication statusPublished - 15 Apr 2011

Keywords

  • crises
  • chaos

Cite this

Predicting Catastrophes in Nonlinear Dynamical Systems by Compressive Sensing. / Wang, Wen-Xu; Yang, Rui; Lai, Ying-Cheng; Kovanis, Vassilios; Grebogi, Celso.

In: Physical Review Letters, Vol. 106, No. 15, 154101, 15.04.2011.

Research output: Contribution to journalArticle

Wang, Wen-Xu ; Yang, Rui ; Lai, Ying-Cheng ; Kovanis, Vassilios ; Grebogi, Celso. / Predicting Catastrophes in Nonlinear Dynamical Systems by Compressive Sensing. In: Physical Review Letters. 2011 ; Vol. 106, No. 15.
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