The DOI matches its Crossref record; 45 of the 45 references it cites were found in a registry or an index.
Synchronization of chaotic systems
Open accessAbstract
We review some of the history and early work in the area of synchronization in chaotic systems. We start with our own discovery of the phenomenon, but go on to establish the historical timeline of this topic back to the earliest known paper. The topic of synchronization of chaotic systems has always been intriguing, since chaotic systems are known to resist synchronization because of their positive Lyapunov exponents. The convergence of the two systems to identical trajectories is a surprise. We show how people originally thought about this process and how the concept of synchronization changed over the years to a more geometric view using synchronization manifolds. We also show that building synchronizing systems leads naturally to engineering more complex systems whose constituents are chaotic, but which can be tuned to output various chaotic signals. We finally end up at a topic that is still in very active exploration today and that is synchronization of dynamical systems in networks of oscillators.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
The chemical basis of morphogenesis
Turing, A. M. (1952) · Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences · doi:10.1098/rstb.1952.0012 · Cited by 11,733
Synchronization in chaotic systems
Pecora, L. M., & Carroll, T. L. (1990) · Physical Review Letters · doi:10.1103/physrevlett.64.821 · Cited by 10,625
Self-citationErgodic theory of chaos and strange attractors
Eckmann, J. P., & Ruelle, D. (1985) · Reviews of Modern Physics · doi:10.1103/revmodphys.57.617 · Cited by 4,941
Singularities and Groups in Bifurcation Theory
Golubitsky, M., Stewart, I., & Schaeffer, D. G. (1988) · Applied Mathematical Sciences · doi:10.1007/978-1-4612-4574-2 · Cited by 2,958
Generalized synchronization of chaos in directionally coupled chaotic systems
Rulkov, N. F., Sushchik, M. M., Tsimring, L. S., & Abarbanel, H. D. I. (1995) · Physical Review E · doi:10.1103/physreve.51.980 · Cited by 1,799
Stability Theory of Synchronized Motion in Coupled-Oscillator Systems
Fujisaka, H., & Yamada, T. (1983) · Progress of Theoretical Physics · doi:10.1143/ptp.69.32 · Cited by 1,355
Driving systems with chaotic signals
Pecora, L. M., & Carroll, T. L. (1991) · Physical Review A · doi:10.1103/physreva.44.2374 · Cited by 1,042
Self-citationGeneralized synchronization of chaos: The auxiliary system approach
Abarbanel, H. D. I., Rulkov, N. F., & Sushchik, M. M. (1996) · Physical Review E · doi:10.1103/physreve.53.4528 · Cited by 650
Cluster synchronization and isolated desynchronization in complex networks with symmetries
Pecora, L. M., Sorrentino, F., Hagerstrom, A. M., Murphy, T. E., & Roy, R. (2014) · Nature Communications · doi:10.1038/ncomms5079 · Cited by 590
Self-citationBubbling of attractors and synchronisation of chaotic oscillators
Ashwin, P., Buescu, J., & Stewart, I. (1994) · Physics Letters A · doi:10.1016/0375-9601(94)90947-4 · Cited by 488
Cited by
Parastesh, F., Jafari, S., Azarnoush, H., Shahriari, Z., Wang, Z., Boccaletti, S., & Perc, M. (2021) · Physics Reports · doi:10.1016/j.physrep.2020.10.003 · Cited by 291
Wang, W., Wang, X., Luo, X., & Yuan, M. (2018) · IEEE Access · doi:10.1109/access.2018.2872745 · Cited by 44
Metadata
- Authors
- Pecora, L. M., & Carroll, T. L.
- Venue
- Chaos: An Interdisciplinary Journal of Nonlinear Science
- Publisher
- AIP Publishing
- Published
- 2015-04-16
- Volume
- 25
- Issue
- 9
- Pages
- 097611-097611
- ISSN
- 1054-1500 (ISSN-L)
- 1089-7682
- OpenAlex
- W2002131976
- Cited by
- 366
- References
- 45
- FWCI
- 20.31
- Type
- journal article
- Language
- en
- Open access
- hybrid
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Synchronization of chaotic systems. https://app.cochat.ai/papers/10.1063/1.4917383
- The paper
- Pecora, L. M., & Carroll, T. L. (2015). Synchronization of chaotic systems. Chaos: An Interdisciplinary Journal of Nonlinear Science. https://doi.org/10.1063/1.4917383
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
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.
