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Driving systems with chaotic signals
Abstract
We generalize the idea of driving a stable system to the situation when the drive signal is chaotic. This leads to the concept of conditional Lyapunov exponents and also generalizes the usual criteria of the linear stability theorem. We show that driving with chaotic signals can be done in a robust fashion, rather insensitive to changes in system parameters. The calculation of the stability criteria leads naturally to an estimate for the convergence of the driven system to its stable state. We focus on a homogeneous driving situation that leads to the construction of synchronized chaotic subsystems. We apply these ideas to the Lorenz and R\"ossler systems, as well as to an electronic circuit and its numerical model.
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Citations
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
Phase Synchronization of Chaotic Oscillators
Rosenblum, M. G., Pikovsky, A. S., & Kurths, J. (1996) · Physical Review Letters · doi:10.1103/physrevlett.76.1804 · Cited by 2,743
Symmetric Ciphers Based on Two-Dimensional Chaotic Maps
Fridrich, J. (1998) · International Journal of Bifurcation and Chaos · doi:10.1142/s021812749800098x · Cited by 1,917
Fundamentals of synchronization in chaotic systems, concepts, and applications
Pecora, L. M., Carroll, T. L., Johnson, G. A., Mar, D. J., & Heagy, J. F. (1997) · Chaos: An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.166278 · Cited by 862
Self-citationSynchronous chaos in coupled oscillator systems
Heagy, J. F., Carroll, T. L., & Pecora, L. M. (1994) · Physical Review E · doi:10.1103/physreve.50.1874 · Cited by 462
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Metadata
- Authors
- Pecora, L. M., & Carroll, T. L.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1991-08-01
- Volume
- 44
- Issue
- 4
- Pages
- 2374-2383
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2094780448
- Cited by
- 1,042
- References
- 0
- FWCI
- 14.10
- Type
- journal article
- Language
- en
- Open access
- closed
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- Pecora, L. M., & Carroll, T. L. (1991). Driving systems with chaotic signals. Physical Review A. https://doi.org/10.1103/physreva.44.2374
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