The DOI matches its Crossref record; 13 of the 13 references it cites were found in a registry or an index.
Mechanism of Time-Delayed Feedback Control
Open accessAbstract
The Pyragas method for controlling chaos is investigated in detail from the experimental as well as theoretical point of view. We show by an analytical stability analysis that the revolution around an unstable periodic orbit governs the success of the control scheme. Our predictions concerning the transient behavior of the control signal are confirmed by numerical simulations and an electronic circuit experiment.
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Citations
Cites
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
Guckenheimer, J., & Holmes, P. (1983) · Applied Mathematical Sciences · doi:10.1007/978-1-4612-1140-2 · Cited by 16,144
Theory of Functional Differential Equations
Hale, J. K. (1977) · Applied Mathematical Sciences · doi:10.1007/978-1-4612-9892-2 · Cited by 6,870
Ott, E., Grebogi, C., & Yorke, J. A. (1990) · Physical Review Letters · doi:10.1103/physrevlett.64.1196 · Cited by 5,431
Continuous control of chaos by self-controlling feedback
Pyragas, K. (1992) · Physics Letters A · doi:10.1016/0375-9601(92)90745-8 · Cited by 3,316
Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
Cowan, J. D. (1986) · Mathematical Biosciences · doi:10.1016/0025-5564(86)90154-9 · Cited by 1,073
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
Ditto, W. L., Rauseo, S. N., & Spano, M. L. (1990) · Physical Review Letters · doi:10.1103/physrevlett.65.3211 · Cited by 711
Stabilizing high-period orbits in a chaotic system: The diode resonator
Hunt, E. R. (1991) · Physical Review Letters · doi:10.1103/physrevlett.67.1953 · Cited by 639
Control of chaos via extended delay feedback
Pyragas, K. (1995) · Physics Letters A · doi:10.1016/0375-9601(95)00654-l · Cited by 440
Stability of periodic orbits controlled by time-delay feedback
Bleich, M. E., & Socolar, J. E. S. (1996) · Physics Letters A · doi:10.1016/0375-9601(95)00827-6 · Cited by 204
Metadata
- Authors
- Just, W., Bernard, T., Ostheimer, M., Reibold, E., & Benner, H.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1997-01-13
- Volume
- 78
- Issue
- 2
- Pages
- 203-206
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1575806465
- Cited by
- 314
- References
- 13
- FWCI
- 14.64
- Type
- journal article
- Language
- en
- Open access
- green
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- Just, W., Bernard, T., Ostheimer, M., Reibold, E., & Benner, H. (1997). Mechanism of Time-Delayed Feedback Control. Physical Review Letters. https://doi.org/10.1103/physrevlett.78.203
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