Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



A note on the uniqueness of the closed orbit of the FitzHugh-Nagumo system

Author: Makoto Hayashi
Journal: Quart. Appl. Math. 58 (2000), 171-176
MSC: Primary 34C25; Secondary 34C60
DOI: https://doi.org/10.1090/qam/1739043
MathSciNet review: MR1739043
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Abstract: A parameter range for which the ordinary differential equations governing the FitzHugh nerve system have a unique nontrivial closed orbit is given. It is wider than those already known.

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

  • [Fi] R. FitzHugh, Impulses and physiological states in theoretical models of nerve membrane, Biophys. J. 1, 445-466 (1961)
  • [H1] M. Hayashi, On the uniqueness of the closed orbit of FitzHugh-Nagumo system, Math. Japon. 46 (2), 331-336 (1997) MR 1479835
  • [H2] M. Hayashi, On the uniqueness of the closed orbit of the Liénard system, Math. Japon. 46 (3), 371-376 (1997) MR 1487283
  • [K-S] E. Kaumann and U. Staude, Uniqueness and nonexistence of limit cycles for the FitzHugh equation, Lecture Notes in Math. 1017, Springer-Verlag, New York, 1983, pp. 313-321 MR 726594
  • [Na] J. Nagumo, S. Arimoto, and S. Yoshizawa, An active pulse transmission line simulating nerve axon, Proc. IRE 50, 2061-2070 (1962)
  • [Su] J. Sugie, Nonexistence of periodic solutions for the FitzHugh nerve system, Quart. Appl. Math. 49, 543-554 (1991) MR 1121685
  • [T-V] S. A. Treskov and E. P. Volokitin, On existence of periodic orbits for the FitzHugh nerve system, Quart. Appl. Math. 54, 601-607 (1996) MR 1417226
  • [Ze-1] X. Zeng, On the uniqueness of limit cycle of Liénard's equation, Scientia Sinica (Series A) 25, 583-592 (1982) MR 670882
  • [Ze-2] X. Zeng, Z. Zhang, and S. Gao, On the uniqueness of the limit cycle of the generalized Liénard equation, Bull. London Math. Soc. 26, 213-247 (1994) MR 1289041

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DOI: https://doi.org/10.1090/qam/1739043
Article copyright: © Copyright 2000 American Mathematical Society

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