Journal of Mathematical Biology

, Volume 22, Issue 1, pp 81–104

Stability of fast travelling pulse solutions of the FitzHugh—Nagumo equations

  • Eiji Yanagida


The FitzHugh-Nagumo equation ut=uxx+f(u)-w, ut=b(u-dw), is a simplified mathematical description of a nerve axon. If the parameters b>0 and d⩾0 are taken suitably, this equation has two travelling pulse solutions with different propagation speeds. We study the stability of the fast pulse solution when b>0 is sufficiently small. It is proved analytically by eigenvalue analysis that the fast pulse solution is “exponentially stable” if d>0, and is “marginally stable” but not exponentially stable if d=0.

Key words

FitzHugh-Nagumo equation pulse solution stability 


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Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Eiji Yanagida
    • 1
  1. 1.Department of Information ScienceKanazawa Institute of TechnologyIshikawaJapan

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