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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References | Similar Articles | Additional Information

**[1]**E. A. Coddington and N. Levinson,*Theory and Ordinary Differential Equations*, McGraw-Hill, New York, 1955 MR**0069338****[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. HsÌu 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. HsÌu,*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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Additional Information

DOI:
https://doi.org/10.1090/qam/1121685

Article copyright:
© Copyright 1991
American Mathematical Society