Abstract:
Patterns in reaction-diffusion systems near primary bifurcations can be studied locally and classified by means of amplitude equations. This is not possible for excitable reaction-diffusion systems. In this paper we propose a global classification of two variable excitable reaction-diffusion systems. In particular, we claim that the topology of the underlying two-dimensional homogeneous dynamics organizes the system's behavior. We believe that this classification provides a useful tool for the modeling of any real system whose microscopic details are unknown. (C) 2000 Published by Elsevier Science B.V.
Registro:
Documento: |
Artículo
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Título: | Towards a global classification of excitable reaction-diffusion systems |
Autor: | Dawson, S.P.; D'Angelo, M.V.; Pearson, J.E. |
Filiación: | Departamento de Física, Facultad de Ciencias Exactas y Naturales, Pabellón i, (1428) Buenos Aires, Argentina Applied Theoretical and Computational Physics, Los Alamos National Laboratory, XCM MS F645, Los Alamos, NM 87545, United States
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Palabras clave: | arithmetic; article; classification; diffusion; dynamics; excitation; flow; geometry; mathematical analysis; model |
Año: | 2000
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Volumen: | 265
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Número: | 5-6
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Página de inicio: | 346
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Página de fin: | 352
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DOI: |
http://dx.doi.org/10.1016/S0375-9601(00)00008-6 |
Título revista: | Physics Letters, Section A: General, Atomic and Solid State Physics
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Título revista abreviado: | Phys Lett Sect A Gen At Solid State Phys
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ISSN: | 03759601
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CODEN: | PYLAA
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03759601_v265_n5-6_p346_Dawson |
Referencias:
- Cross, M.C., Hohenberg, P.C., (1993) Rev. Mod. Phys., 65, p. 851
- Lee, K.J., (1993) Science, 261, p. 192
- Lee, K.J., (1994) Nature, 369, p. 215
- Lee, K.J., Swinney, H.L., (1995) Phys. Rev. E, 51, p. 1899
- Pearson, J.E., (1993) Science, 261, p. 189
- Muratov, C.B., Osipov, V.V., (1996) Phys. Rev. E, 54, p. 4860
- Guckenheimer, J., Holmes, P., (1986), Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer, New York; Ondarcuhu, T., (1993) Phys. Rev. Lett., 70, pp. 3892-3895
- Fitzhugh, R., (1960) J. Gen. Physiol., 43, p. 876
- Eguia, M., Phys. Rev. E.
- Hirsch, M.W., Smale, S., (1974), p. 239. , Differential equations, dynamical systems, and linear algebra, Academic Press, San Diego; D'Angelo, M.V., Dawson, S.P., Pearson, J.E., in preparation; Edblom, E.C., Orban, M., Epstein, I.R., (1986) J. Am. Chem. Soc., 108, p. 2826
- Gaspar, V., Showalter, K., (1990) J. Phys. Chem., 94, p. 4973
- Gaspar, V., Showalter, K., (1987) J. Phys. Chem., 109, p. 4869
- Reynolds, W., (1994) Phys. Rev. Lett., 72, p. 2797
- Reynolds, W., (1997) Phys. Rev. E, 56, p. 185
- Hagberg, A., Meron, E., (1994) Chaos, 4, p. 477
- Doelman, A., Kaper, T.J., Zegeling, P.A., (1997) Nonlinearity, 10, pp. 523-563
- Pearson, J.E., Horsthemke, W., (1989) J. Chem. Phys., 90, p. 1588
- Argentina, M., Coullet, P., Mahadevan, L., (1997) Phys. Rev. Lett., 79, p. 2803
Citas:
---------- APA ----------
Dawson, S.P., D'Angelo, M.V. & Pearson, J.E.
(2000)
. Towards a global classification of excitable reaction-diffusion systems. Physics Letters, Section A: General, Atomic and Solid State Physics, 265(5-6), 346-352.
http://dx.doi.org/10.1016/S0375-9601(00)00008-6---------- CHICAGO ----------
Dawson, S.P., D'Angelo, M.V., Pearson, J.E.
"Towards a global classification of excitable reaction-diffusion systems"
. Physics Letters, Section A: General, Atomic and Solid State Physics 265, no. 5-6
(2000) : 346-352.
http://dx.doi.org/10.1016/S0375-9601(00)00008-6---------- MLA ----------
Dawson, S.P., D'Angelo, M.V., Pearson, J.E.
"Towards a global classification of excitable reaction-diffusion systems"
. Physics Letters, Section A: General, Atomic and Solid State Physics, vol. 265, no. 5-6, 2000, pp. 346-352.
http://dx.doi.org/10.1016/S0375-9601(00)00008-6---------- VANCOUVER ----------
Dawson, S.P., D'Angelo, M.V., Pearson, J.E. Towards a global classification of excitable reaction-diffusion systems. Phys Lett Sect A Gen At Solid State Phys. 2000;265(5-6):346-352.
http://dx.doi.org/10.1016/S0375-9601(00)00008-6