The DOI matches its Crossref record; 13 of the 13 references it cites were found in a registry or an index.
Weak and strong synchronization of chaos
Abstract
It is shown that synchronization in unidirectionally coupled chaotic systems develops in two stages as the coupling strength is increased. The first stage is characterized by a weak synchronization, i.e., a response system subjected to a driving system undergoes a transition and exhibits a behavior completely insensitive to initial conditions. Further increase of the coupling strength causes the dimension decrease of the overall dynamics and leads finally to a strong synchronization. In this stage, the dimension of the strange attractor in the full phase space of the two systems saturates to the dimension of the driving attractor.
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Citations
Cites
Deterministic Nonperiodic Flow
Lorenz, E. N. (1963) · Journal of the Atmospheric Sciences · doi:10.1175/1520-0469(1963)020<0130:dnf>2.0.co;2 · Cited by 19,398
Synchronization in chaotic systems
Pecora, L. M., & Carroll, T. L. (1990) · Physical Review Letters · doi:10.1103/physrevlett.64.821 · Cited by 10,625
Characterization of Strange Attractors
Grassberger, P., & Procaccia, I. (1983) · Physical Review Letters · doi:10.1103/physrevlett.50.346 · Cited by 4,857
An equation for continuous chaos
Rössler, O. E. (1976) · Physics Letters A · doi:10.1016/0375-9601(76)90101-8 · Cited by 4,012
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
Dimension increase in filtered chaotic signals
Badii, R., Broggi, G., Derighetti, B., Ravani, M., Ciliberto, S., Politi, A., & Rubio, M. A. (1988) · Physical Review Letters · doi:10.1103/physrevlett.60.979 · Cited by 220
Predictable chaos in slightly perturbed unpredictable chaotic systems
Pyragas, K. (1993) · Physics Letters A · doi:10.1016/0375-9601(93)90640-l · Cited by 214
Self-citationEstimating correlation dimension from a chaotic time series: when does plateau onset occur?
Ding, M., Grebogi, C., Ott, E., et al. (1993) · Physica D Nonlinear Phenomena · doi:10.1016/0167-2789(93)90103-8 · Cited by 195
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
Explosive transitions in complex networks’ structure and dynamics: Percolation and synchronization
Boccaletti, S., Almendral, J. A., Guan, S., Leyva, I., Liu, Z., Sendiña-Nadal, I., Wang, Z., & Zou, Y. (2016) · Physics Reports · doi:10.1016/j.physrep.2016.10.004 · Cited by 363
Generalized synchrony of coupled stochastic processes with multiplicative noise
Jafri, H. H., Singh, R. K. B., & Ramaswamy, R. (2016) · Physical Review E · doi:10.1103/physreve.94.052216 · Cited by 12
Metadata
- Authors
- Pyragas, K.
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 1996-11-01
- Volume
- 54
- Issue
- 5
- Pages
- R4508-R4511
- ISSN
- 1063-651X (ISSN-L)
- 1095-3787
- OpenAlex
- W2127533144
- Cited by
- 293
- References
- 13
- FWCI
- 4.81
- Type
- journal article
- Language
- en
- Open access
- closed
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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.
