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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



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
MathSciNet review: 508454
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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.
  • 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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