5 Citations (Scopus)

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

Fingerprint

Nonlinear dynamical systems
Compressive Sensing
Nonlinear Dynamical Systems
forecasting
dynamical systems
Forecasting
Time-varying
Sustainability
Series Expansion
Sustainable development
Attractor
Time series
Dynamical systems
Dynamical system
Paradigm
series expansion
Unknown
Demonstrate
Influence
Framework

ASJC Scopus subject areas

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

Cite this

Forecasting the future : Is it possible for adiabatically time-varying nonlinear dynamical systems? / Yang, Rui; Lai, Ying-Cheng; Grebogi, Celso.

In: Chaos, Vol. 22, No. 3, 033119, 05.07.2012.

Research output: Contribution to journalArticle

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