Dynamic Analysis of FitzHugh-Nagumo System

• Wenzhe Cui ^[1]
  1. [1] Sun Yat-sen University

     Sun Yat-sen University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 5, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we prove the existence of traveling train and impulse in FitzHughNagumo system ut = ux x − u(u − 1)(u − a) − v, vt = ε(u − γv) by studying a saddle-node bifurcation and a Bogdanov-Takens bifurcation of the corresponding three-dimensional system x˙ = z, y˙ = b(x − dy), z˙ = x(x − 1)(x − a) + y + cz.

    The bifurcation analysis of the three-dimensional system indicates that the number of steady-state solutions in FitzHugh-Nagumo system can change through saddle-node bifurcation of the three-dimensional system, and there are different parameter values for which the three-dimensional system can have a limit cycle or a homoclinic loop, which implies that FitzHugh-Nagumo system can have a traveling train or an impulse for some specific parameters.

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