Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Bulletin of the American Mathematical Society
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
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • 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), no. 3, 515–523. MR 0484504 (58 #4408)
  • 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), no. 9, 881–895. MR 0381744 (52 #2633)
  • 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. 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 0025140 (9,604a)
  • 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.

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1970): 34C25, 35B10, 35Q99, 92A15, 35C05, 34E99, 35A35, 39A10

Retrieve articles in all journals with MSC (1970): 34C25, 35B10, 35Q99, 92A15, 35C05, 34E99, 35A35, 39A10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9904-1978-14560-1
PII: S 0002-9904(1978)14560-1