Pattern formation and periodic structures in systems modeled by reaction-diffusion equations

Authors:
J. M. Greenberg, B. D. Hassard and S. P. Hastings

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

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References | Similar Articles | Additional Information

**1.**R. FitzHugh,*Mathematical models of excitation and propagation in nerve*, Biological Engineering, H. P. Schwan (ed.), McGraw-Hill, New York, 1969.**2.**J. M. Greenberg and S. P. Hastings,*Spatial patterns for discrete models of diffusion in excitable media*, SIAM J. Appl. Math. 34 (1978). MR**484504****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).**4.**S. P. Hastings,*Some mathematical problems from neurobiology*, Amer. Math. Monthly 82 (1975), 881-895. MR**381744****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.**7.**N. Wiener and A. 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. Mexico 16 (1946), 205-265. 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.

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DOI:
https://doi.org/10.1090/S0002-9904-1978-14560-1