title: Predicting catastrophes in nonlinear dynamical systems by compressive sensing.
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.
authors.affiliation: School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA. wenxuw@gmail.com
authors.forename: Wen-Xu
authors.initials: WX
authors.lastname: Wang
authors.forename: Rui
authors.initials: R
authors.lastname: Yang
authors.forename: Ying-Cheng
authors.initials: YC
authors.lastname: Lai
authors.forename: Vassilios
authors.initials: V
authors.lastname: Kovanis
authors.forename: Celso
authors.initials: C
authors.lastname: Grebogi