The Relaxational Oscillation Solution for Fitzhugh’s Nerve Conduction Equation

Lin Chang; Li Ji-bin; Liu Zeng-rong

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1985 > 6(12): 1079-1086

Lin Chang, Li Ji-bin, Liu Zeng-rong. The Relaxational Oscillation Solution for Fitzhugh’s Nerve Conduction Equation[J]. Applied Mathematics and Mechanics, 1985, 6(12): 1079-1086.

Citation:

Lin Chang, Li Ji-bin, Liu Zeng-rong. The Relaxational Oscillation Solution for Fitzhugh’s Nerve Conduction Equation[J]. Applied Mathematics and Mechanics, 1985, 6(12): 1079-1086.

Citation:

Lin Chang, Li Ji-bin, Liu Zeng-rong. The Relaxational Oscillation Solution for Fitzhugh’s Nerve Conduction Equation[J]. Applied Mathematics and Mechanics, 1985, 6(12): 1079-1086.

PDF( 2504 KB)

The Relaxational Oscillation Solution for Fitzhugh’s Nerve Conduction Equation

1.
Anhui University, Hefei;
2.
Kunming Engineering Institute, Kunming

Received Date: 1984-11-14
Publish Date: 1985-12-15

Abstract

Abstract

By using the matching asymptotic method, we calculated the analytic expression of relaxational osillation sochition for Fitznugr's nerve conduction equation, oscillation period and the parametric region in which the relaxational oscillation occurs.

FullText(HTML)

References(8)

References

[1]	Fitzhugh,R.,Thresholds and plateaus in the Hodgkin-Huxley nerve equations,J.Gen.Phys.,43(1960).
[2]	Troy,W.C.,Bifurcation phenomena in Fitzhugh's nerve conduction equation,J.Math.Anal.Appl.,54(1976),678-690.
[3]	Hsü,I.D.and N.D.Kazarinoff,An applicable Hopf bifurcation formula and instability of small periodic solutions of the Field-Noyes model,J.Math.Anal.Appl.,55(1976),61-89.
[4]	Hsü,I.D.,A higher order Hopf bifurcation formula and its application to Fitzhugh's nerve conduction equations,J.Math.Anal.Appl.,60,1(1977),47-57.
[5]	Hadeler,K.P.,etc.,Generation of the nervous impulse and periodic oscillations,Biol.Cybernet.,23(1976),211-218.
[6]	G(?)bber,F.and K.D.Willamowski,Liapunov approach to multiple Hopf bifurcation,J Math.Anal.Appl.,71(1979),333-350.
[7]	Negrini,P.and L.Salvadori,Attraction and Hopf bifurcation,Nonlinear Analysis,3,1(1979),87-99.
[8]	Okuda,M.,A new method of nonlinear analysis for threshold and shaping actions in transient states,Prog.Theory Phys.,66,1(1981),90-100．