Pattern formation and periodic structures in systems modeled by reaction-diffusion equations
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- by J. M. Greenberg, B. D. Hassard and S. P. Hastings PDF
- Bull. Amer. Math. Soc. 84 (1978), 1296-1327
References
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1. R. FitzHugh, Mathematical models of excitation and propagation in nerve, Biological Engineering, H. P. Schwan (ed.), McGraw-Hill, New York, 1969.
- J. M. Greenberg and S. P. Hastings, Spatial patterns for discrete models of diffusion in excitable media, SIAM J. Appl. Math. 34 (1978), no. 3, 515–523. MR 484504, DOI 10.1137/0134040 3. J. M. Greenberg, C. Greene, and S. P. Hastings, A combinatorial problem arising in the study of reaction-diffusion equations, SIAM J. Appl. Math, (to appear).
- S. P. Hastings, Some mathematical problems from neurobiology, Amer. Math. Monthly 82 (1975), no. 9, 881–895. MR 381744, DOI 10.2307/2318490 5. J. Nagumo, S. Yoshizawa, and S. Arimoto, Bistable transmission lines, IEEE Trans. Comm. Tech. 12 (1965), 400. 6. L. V. Reshodko, and S. Bures, Computer simulation of reverberating spreading depression in a network of cell automata, Biol. Cybernet. 18 (1975), 181-190.
- Norbert Wiener and Arturo Rosenblueth, The mathematical formulation of the problem of conduction of impulses in a network of connected excitable elements, specifically in cardiac muscle, Arch. Inst. Cardiol. México 16 (1946), 205–265 (English, with Spanish summary). MR 25140 8. A. T. Winfree, Wavelike activity in biological and biochemical media, Lecture Notes in Biomathematics, P. van den Driessche (ed.), Springer-Verlag, Berlin, 1974, p. 241.
Additional Information
- Journal: Bull. Amer. Math. Soc. 84 (1978), 1296-1327
- MSC (1970): Primary 34C25, 35B10, 35Q99, 92A15; Secondary 35C05, 34E99, 35A35, 39A10
- DOI: https://doi.org/10.1090/S0002-9904-1978-14560-1
- MathSciNet review: 508454