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Spatial Patterns for Discrete Models of Diffusion in Excitable Media
Abstract
In a spatially homogeneous environment an excitable media is characterized by a globally stable equilibrium state, and also by a threshold mechanism which produces a large amplitude response to a sufficiently large stimulus. This response is temporary, however, and the system soon returns to its equilibrium configuration. Such media are to be distinguished from oscillatory ones; the latter support self-excited spatially homogeneous oscillations. In this paper we show how spatial inhomogeneities in an excitable media tend to organize themselves to produce spatial patterns which oscillate periodically in time.
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Cites
The chemical basis of morphogenesis
Turing, A. M. (1952) · Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences · doi:10.1098/rstb.1952.0012 · Cited by 11,733
Concentration Wave Propagation in Two-dimensional Liquid-phase Self-oscillating System
ZAIKIN, A. N., & ZHABOTINSKY, A. M. (1970) · Nature · doi:10.1038/225535b0 · Cited by 1,903
Traveling bands of chemotactic bacteria: A theoretical analysis
Keller, E. F., & Segel, L. A. (1971) · Journal of Theoretical Biology · doi:10.1016/0022-5193(71)90051-8 · Cited by 1,134
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Biological Oscillators: their Mathematical Analysis
(1973) · Elsevier eBooks · doi:10.1016/b978-0-12-547350-7.x5001-9 · Cited by 445
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Cited by
Statistical physics of social dynamics
Castellano, C., Fortunato, S., & Loreto, V. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.591 · Cited by 4,119
Haimovici, A., Tagliazucchi, E., Balenzuela, P., & Chialvo, D. R. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.178101 · Cited by 438
Synchronous and asynchronous updating in cellular automata
Schönfisch, B., & de Roos, A. (1999) · Biosystems · doi:10.1016/s0303-2647(99)00025-8 · Cited by 299
The Origin of Life: Chemical Evolution of a Metabolic System in a Mineral Honeycomb?
Branciamore, S., Gallori, E., Szathmáry, E., & Czárán, T. (2009) · Journal of Molecular Evolution · doi:10.1007/s00239-009-9278-6 · Cited by 63
Metadata
- Authors
- Greenberg, J. M., & Hastings, S. P.
- Venue
- SIAM Journal on Applied Mathematics
- Published
- 1978-05
- Volume
- 34
- Issue
- 3
- Pages
- 515-523
- ISSN
- 0036-1399 (ISSN-L)
- 1095-712X
- OpenAlex
- W1971260725
- Cited by
- 332
- References
- 6
- FWCI
- 5.94
- 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.
