The DOI matches its Crossref record; 79 of the 79 references it cites were found in a registry or an index.
Chaos as an intermittently forced linear system
Open accessAbstract
Understanding the interplay of order and disorder in chaos is a central challenge in modern quantitative science. Approximate linear representations of nonlinear dynamics have long been sought, driving considerable interest in Koopman theory. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work combines delay embedding and Koopman theory to decompose chaotic dynamics into a linear model in the leading delay coordinates with forcing by low-energy delay coordinates; this is called the Hankel alternative view of Koopman (HAVOK) analysis. This analysis is applied to the Lorenz system and real-world examples including Earth’s magnetic field reversal and measles outbreaks. In each case, forcing statistics are non-Gaussian, with long tails corresponding to rare intermittent forcing that precedes switching and bursting phenomena. The forcing activity demarcates coherent phase space regions where the dynamics are approximately linear from those that are strongly nonlinear.
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Data-driven discovery of partial differential equations
Rudy, S. H., Brunton, S. L., Proctor, J. L., & Kutz, J. N. (2017) · Science Advances · doi:10.1126/sciadv.1602614 · Cited by 1,557
Self-citationData-driven discovery of coordinates and governing equations
Champion, K., Lusch, B., Kutz, J. N., & Brunton, S. L. (2019) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1906995116 · Cited by 909
Self-citation(2018) · IEEE Control Systems · doi:10.1109/mcs.2018.2810460 · Cited by 518
Data-Driven Aerospace Engineering: Reframing the Industry with Machine Learning
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Self-citationDiscovery of nonlinear multiscale systems: Sampling strategies and embeddings
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Metadata
- Authors
- Brunton, S. L., Brunton, B. W., Proctor, J. L., Kaiser, E., & Kutz, J. N.
- Venue
- Nature Communications
- Published
- 2017-05-30
- Volume
- 8
- Issue
- 1
- Pages
- 19-19
- ISSN
- 2041-1723 (ISSN-L)
- OpenAlex
- W2510030309
- Cited by
- 608
- References
- 79
- FWCI
- 22.45
- Type
- journal article
- Language
- en
- Open access
- gold
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