On existence of periodic orbits for the FitzHugh nerve system

Quarterly of Applied Mathematics

Volumn 54, Issue 4, 1996, Pages 601-607

  Treskov, S A ^a   Volokitin, E P ^a  

^a SOBOLEV INSTITUTE OF MATHEMATICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); MATHEMATICAL MODELS;

FITZHUGH DIFFERENTIAL SYSTEM;

DIFFERENTIAL EQUATIONS;

EID: 0030421273     PISSN: 0033569X     EISSN: None     Source Type: Journal    
DOI: 10.1090/qam/1417226     Document Type: Article

References (8)

1. R. FitzHugh, Impulses and physiological states in theoretical models of nerve membrane, Biophys. J. 1, 445-466 (1961)
2. J. Sugie, Nonexistence of periodic solutions for the FitzHugh nerve system, Quart. Appl. Math. 49, 543-554 (1991)
3. K. P. Hadeler, U. an der Heiden, and K. Schumacher, Generation of the nervous impulse and periodic oscillations, Biol. Cybernet. 23, 211-218 (1976)
4. 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
5. V. I. Arnold, Geometrical Methods in the Theory of Ordinary Differential Equations, Springer-Verlag, New York, 1982 (Russian original, Nauka, Moscow, 1977)
6. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York, 1986, p. 459
7. N. N. Bautin and E. A. Leontovich, Methods and Ways (Examples) of the Qualitative Analysis of Dynamical Systems in a Plane, Nauka, Moscow, 1990, p. 480 (in Russian)
8. A. I. Chibnik and E. E. Shnol, Software for Qualitative Analysis of Differential Equations, Research Computer Center, USSR Academy of Sciences, Pushcino, 1982, p. 10 (in Russian)