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Predicting catastrophes in nonlinear dynamical systems by compressive sensing

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arxiv 1105.0462 v1 pith:IKMWYLSJ submitted 2011-05-03 physics.data-an

Wen-Xu Wang , Rui Yang , Ying-Cheng Lai , Vassilios Kovanis , Celso Grebogi This is my paper · ORCID
classification physics.data-an
keywords catastrophesdynamicalsystemsystemsideanonlinearpredictingseries
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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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