Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 
 

 

Nonexistence of periodic solutions for the FitzHugh nerve system


Author: Jitsuro Sugie
Journal: Quart. Appl. Math. 49 (1991), 543-554
MSC: Primary 92C20; Secondary 34C25
DOI: https://doi.org/10.1090/qam/1121685
MathSciNet review: MR1121685
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  • [2] R. FitzHugh, Thresholds and plateaus in the Hodgkin-Huxley nerve equations, J. Gen. Phys. 43, 867-896 (1960)
  • [3] R. FitzHugh, Impulses and physiological states in theoretical models of nerve membrane, Biophys. J. 1, 445-466 (1961)
  • [4] K. P. Hadeler, U. an der Heiden, and K. Schumacher, Generation of the nervous impulse and periodic oscillations, Biol. Cybernet. 23, 211-218 (1976) MR 0496806
  • [5] I. D. Hs̈u and N. D. Kazarinoff, An applicable Hopf bifurcation formula and instability of small periodic solutions of Field-Noyes model, J. Math. Anal. Appl. 55, 61-89 (1976) MR 0466758
  • [6] I. D. Hs̈u, A higher-order Hopf bifurcation formula and its application to FitzHugh's nerve conduction equations, J. Math. Anal. Appl. 60, 47-57 (1977) MR 0470350
  • [7] E. Kaumann and U. Staude, Uniqueness and nonexistence of limit cycles for the FitzHugh equation, Equadiff 82 (H. W. Knobloch and K. Schmitt, eds.), Lecture Notes in Math., vol. 1017, Springer-Verlag, 1983, pp. 313-321 MR 726594
  • [8] J. Sugie and T. Hara, Non-existence of periodic solutions of the Liénard system, scheduled for J. Math. Anal. Appl. 159, No. 1 (1991) MR 1119432
  • [9] W. C. Troy, Bifurcation phenomena in FitzHugh's nerve conduction equations, J. Math. Anal. Appl. 54, 678-690 (1976) MR 0411683

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DOI: https://doi.org/10.1090/qam/1121685
Article copyright: © Copyright 1991 American Mathematical Society

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