Forecasting the future: Is it possible for adiabatically time-varying nonlinear dynamical systems?

Rui Yang, Ying-Cheng Lai, Celso Grebogi

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

Nonlinear dynamical systems in reality are often under environmental influences that are time-dependent. To assess whether such a system can perform as desired or as designed and is sustainable requires forecasting its future states and attractors based solely on time series. We propose a viable solution to this challenging problem by resorting to the compressive-sensing paradigm. In particular, we demonstrate that, for a dynamical system whose equations are unknown, a series expansion in both dynamical and time variables allows the forecasting problem to be formulated and solved in the framework of compressive sensing using only a few measurements. We expect our method to be useful in addressing issues of significant current concern such as the sustainability of various natural and man-made systems.

Original languageEnglish (US)
Article number033119
JournalChaos
Volume22
Issue number3
DOIs
StatePublished - Jul 5 2012

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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