The DOI matches its Crossref record; 22 of the 22 references it cites were found in a registry or an index.
A Geometrical Theory for Spiral Waves in Excitable Media
Abstract
In this paper, we develop a geometrical theory for waves in excitable reacting media. Using singular perturbation arguments and dispersion of traveling plane wave trains, we derive an approximate theory of wave front propagation which has strong resemblance to the geometrical diffraction theory of high frequency waves in hyperbolic systems, governed by the eikonal equation. Using this theory, we study the effect of curvature on waves in excitable media, specifically, rotating spiral patterns in planar regions. From this theory we are able to determine the frequency and wavelength for spiral patterns in excitable, nonoscillatory media.
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Cites
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Whiteman, K. J. (1975) · Physics Bulletin · doi:10.1088/0031-9112/26/11/028 · Cited by 7,064
Impulses and Physiological States in Theoretical Models of Nerve Membrane
FitzHugh, R. (1961) · Biophysical Journal · doi:10.1016/s0006-3495(61)86902-6 · Cited by 6,258
The Geometry of Biological Time
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Geometrical Theory of Diffraction*
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A computer model of atrial fibrillation
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Spiral Waves of Chemical Activity
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Circus movement in rabbit atrial muscle as a mechanism of trachycardia.
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Cited by
Pattern formation outside of equilibrium
Cross, M. C., & Hohenberg, P. C. (1993) · Reviews of Modern Physics · doi:10.1103/revmodphys.65.851 · Cited by 7,859
Singular perturbation theory of traveling waves in excitable media (a review)
Tyson, J. J., & Keener, J. P. (1988) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(88)90062-0 · Cited by 746
Self-citationPattern formation in excitable media
Meron, E. (1992) · Physics Reports · doi:10.1016/0370-1573(92)90098-k · Cited by 428
A single-pool model for intracellular calcium oscillations and waves in the Xenopus laevis oocyte
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Metadata
- Authors
- Keener, J. P.
- Venue
- SIAM Journal on Applied Mathematics
- Published
- 1986-12
- Volume
- 46
- Issue
- 6
- Pages
- 1039-1056
- ISSN
- 0036-1399 (ISSN-L)
- 1095-712X
- OpenAlex
- W1963936865
- Cited by
- 270
- References
- 22
- FWCI
- 10.66
- 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.
