Predicting Catastrophes in Nonlinear Dynamical Systems by Compressive Sensing

2011/04/15 by Wen-Xu Wang, Rui Yang, Ying‐Cheng Lai +3 · 358 citations
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Artificial intelligence #Chaos control and synchronization #Chaotic #Compressed sensing #Computer science #Dynamical system (definition) #Dynamical systems theory #Field (mathematics) #Fractal and DNA sequence analysis #Function (biology) #Geology #Mathematical analysis #Mathematics #Nonlinear dynamical systems #Nonlinear system #Physics #Series (stratigraphy) #Series expansion #Sparse and Compressive Sensing Techniques #Statistical physics #physics.data-an

paper · pdf · doi:10.1103/physrevlett.106.154101

published in Physical Review Letters 106(15), 154101 (American Physical Society) · accepted by PRL

openalex publication_date 2011/04/15 · arxiv created 2011/05/03 · arxiv updated 2015/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Compressive Sensing [Lecture Notes]
• An Introduction To Compressive Sampling [A sensing/sampling paradigm that goes against the common knowledge in data acquisition]
• Deterministic Nonperiodic Flow
• A universal instability of many-dimensional oscillator systems
• Stable signal recovery from incomplete and inaccurate measurements
• Proceedings of the International Congress of Mathematicians
• Compressed sensing

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