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From attractor to chaotic saddle: a tale of transverse instability
Open accessAbstract
Suppose that a dynamical system possesses an invariant submanifold, and the restriction of the system to this submanifold has a chaotic attractor A. Under which conditions is A an attractor for the original system, and in what sense? We characterize the transverse dynamics near A in terms of the normal Liapunov spectrum of A. In particular, we emphasize the role of invariant measures on A. Our results identify the points at which A: (1) ceases to be asymptotically stable, possibly developing a locally riddled basin; (2) ceases to be an attractor; (3) becomes a transversely repelling chaotic saddle. We show, in the context of what we call `normal parameters' how these transitions can be viewed as being robust. Finally, we discuss some numerical examples displaying these transitions.
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Cites
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Cited by
The synchronization of chaotic systems
Boccaletti, S., Kurths, J., Osipov, G., Valladares, D. L., & Zhou, C. S. (2002) · Physics Reports · doi:10.1016/s0370-1573(02)00137-0 · Cited by 2,764
Fundamentals of synchronization in chaotic systems, concepts, and applications
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Synchronization of chaotic systems
Pecora, L. M., & Carroll, T. L. (2015) · Chaos: An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.4917383 · Cited by 366
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A Dynamical Systems Hypothesis of Schizophrenia
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Metadata
- Authors
- Ashwin, P., Buescu, J., & Stewart, I.
- Venue
- Nonlinearity
- Publisher
- IOP Publishing
- Published
- 1996-05-01
- Volume
- 9
- Issue
- 3
- Pages
- 703-737
- ISSN
- 0951-7715 (ISSN-L)
- 1361-6544
- OpenAlex
- W2030381387
- Cited by
- 349
- References
- 32
- FWCI
- 42.18
- Type
- journal article
- Language
- en
- Open access
- bronze
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
