Predicting catastrophes in nonlinear dynamical systems by compressive sensing

Details Predicting catastrophes in nonlinear dynamical systems by compressive sensing Predicting catastrophes in nonlinear dynamical systems by compressive sensing

2011-05-03

arxiv.org/abs/1105.0462v1

Physics

Data Analysis, Statistics and Probability

accepted by PRL

Scientific paper

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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