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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

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

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A threshold for a caricature of the nerve equation
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by H. P. McKean and V. Moll PDF
Bull. Amer. Math. Soc. 12 (1985), 255-259
References
  • Hirsh Cohen, Mathematical developments in Hodgkin-Huxley theory and its approximations, Some mathematical questions in biology, VII (Proc. Ninth Sympos. Math. Biol., New York, 1975) Lectures on Math. in the Life Sciences, Vol. 8, Amer. Math. Soc., Providence, R.I., 1976, pp. 89–124. MR 0469315
  • John A. Feroe, Traveling waves of infinitely many pulses in nerve equations, Math. Biosci. 55 (1981), no. 3-4, 189–203. MR 627953, DOI 10.1016/0025-5564(81)90095-X
  • Paul C. Fife and J. B. McLeod, The approach of solutions of nonlinear diffusion equations to travelling front solutions, Arch. Rational Mech. Anal. 65 (1977), no. 4, 335–361. MR 442480, DOI 10.1007/BF00250432
    • R. Fitzhugh, Impulses and physiological states in theoretical models of nerve membrane, Biophys. J. 1 (1961), 445-466. R. Fitzhugh, Mathematical models of excitation and propagation in nerve, Biological Engineering (H. Schwan, ed.), 1969, pp. 1-85.
  • K. P. Hadeler, Nonlinear diffusion equations in biology, Ordinary and partial differential equations (Proc. Fourth Conf., Univ. Dundee, Dundee, 1976) Lecture Notes in Math., Vol. 564, Springer, Berlin, 1976, pp. 163–206. MR 0526382
    • A. L. Hodgkin, The conduction of the nervous impulse, Liverpool Univ. Press, Liverpool, 1971. A. L. Hodgkin and A. F. Huxley, A qualitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol. 117 (1952), 500-544.
  • H. P. McKean Jr., Nagumo’s equation, Advances in Math. 4 (1970), 209–223 (1970). MR 260438, DOI 10.1016/0001-8708(70)90023-X
  • H. P. McKean, Stabilization of solutions of a caricature of the FitzHugh-Nagumo equation, Comm. Pure Appl. Math. 36 (1983), no. 3, 291–324. MR 697467, DOI 10.1002/cpa.3160360303
    • J. Nagumo, S. Arimoto and S. Yoshizawa, An active pulse transmission line simulating nerve axon, Proc. IRE 50 (1964), 2061-2070.
  • John Rinzel, Simple model equations for active nerve conduction and passive neuronal integration, Some mathematical questions in biology, VII (Proc. Ninth Sympos. Math. Biol., New York, 1975) Lectures on Math. in the Life Sciences, Vol. 8, Amer. Math. Soc., Providence, R.I., 1976, pp. 125–164. MR 0469324
  • David Terman, Threshold phenomena for a reaction-diffusion system, J. Differential Equations 47 (1983), no. 3, 406–443. MR 692838, DOI 10.1016/0022-0396(83)90043-8
  • David Terman, A free boundary problem arising from a bistable reaction-diffusion equation, SIAM J. Math. Anal. 14 (1983), no. 6, 1107–1129. MR 718812, DOI 10.1137/0514086
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Additional Information
  • Journal: Bull. Amer. Math. Soc. 12 (1985), 255-259
  • MSC (1980): Primary 35K55, 35Q20; Secondary 92A09
  • DOI: https://doi.org/10.1090/S0273-0979-1985-15367-4
  • MathSciNet review: 776480