The DOI matches its Crossref record; 9 of the 9 references it cites were found in a registry or an index.
Chaotic states and routes to chaos in the forced pendulum
Abstract
An experimental study of the chaotic states and the routes to chaos in the driven pendulum as simulated by a phase-locked-loop electronic circuit is presented. For a particular value of the quality factor ($Q=4$), for which the chaotic behavior is found to be rich in structure, the state diagram (phase locked or unlocked) is established as a function of driving frequency and amplitude, and the nature of the chaos in these states is investigated and discussed in light of recent models of chaos in dynamical systems. The driven pendulum is found to exhibit symmetry breaking as a precursor to the period-doubling route for chaos. Although period doubling is found to be fairly common in the phase-locked states of the pendulum, it does not always manifest itself in complete bifurcation cascades. Intermittent behavior between two unstable phase-locked states is also commonly observed.
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Cites
Handbook of Mathematical Functions
(2018) · A Century of Excellence in MEASUREMENTS, STANDARDS, and TECHNOLOGY · doi:10.1201/9781351069397-39 · Cited by 9,062
A two-dimensional mapping with a strange attractor
Hénon, M. (1976) · Communications in Mathematical Physics · doi:10.1007/bf01608556 · Cited by 2,987
Ruelle, D., & Takens, F. (1971) · Communications in Mathematical Physics · doi:10.1007/bf01646553 · Cited by 2,769
Effect of ac Impedance on dc Voltage-Current Characteristics of Superconductor Weak-Link Junctions
McCumber, D. E. (1968) · Journal of Applied Physics · doi:10.1063/1.1656743 · Cited by 1,441
Intermittency and the Lorenz model
Manneville, P., & Pomeau, Y. (1979) · Physics Letters A · doi:10.1016/0375-9601(79)90255-x · Cited by 412
Noise phenomena in Josephson junctions
Huberman, B. A., Crutchfield, J. P., & Packard, N. H. (1980) · Applied Physics Letters · doi:10.1063/1.92020 · Cited by 363
Self-citationHirsch, J. E., Huberman, B. A., & Scalapino, D. J. (1982) · Physical Review A · doi:10.1103/physreva.25.519 · Cited by 358
Self-citationChaotic States of Anharmonic Systems in Periodic Fields
Huberman, B. A., & Crutchfield, J. P. (1979) · Physical Review Letters · doi:10.1103/physrevlett.43.1743 · Cited by 282
Self-citationChaos and noise rise in Josephson junctions
Pedersen, N. F., & Davidson, A. (1981) · Applied Physics Letters · doi:10.1063/1.92574 · Cited by 140
Cited by
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
Lackner, J. R., & DiZio, P. (1992) · The Head-Neck Sensory Motor System · doi:10.1093/acprof:oso/9780195068207.003.0033 · Cited by 11
Metadata
- Authors
- D'Humieres, D., Beasley, M. R., Huberman, B. A., & Libchaber, A.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1982-12-01
- Volume
- 26
- Issue
- 6
- Pages
- 3483-3496
- ISSN
- 0556-2791 (ISSN-L)
- OpenAlex
- W2058236317
- Cited by
- 490
- References
- 9
- FWCI
- 21.80
- Type
- journal article
- Language
- en
- Open access
- closed
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- D'Humieres, D., Beasley, M. R., Huberman, B. A., & Libchaber, A. (1982). Chaotic states and routes to chaos in the forced pendulum. Physical Review A. https://doi.org/10.1103/physreva.26.3483
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