Simulación Numérica de Ondas Viajeras del Sistema FitzHugh-Nagumo

• Rubio-Mercedes, C.E. ^[1] ; Barbosa Verao, Glauce ^[2]
  1. [1] UEMS-Universidade Estadual de Mato Grosso do Sul, Dourados, MS, Brasil
  2. [2] USP-Universidade de São Paulo, São Paulo, Brasil
• Localización: Selecciones Matemáticas, ISSN-e 2411-1783, Vol. 5, Nº. 2 (Agosto - Diciembre), 2018, págs. 193-203
• Idioma: español
• DOI: 10.17268/sel.mat.2018.02.06
• Títulos paralelos:
  • Numerical Simulation of Traveling Waves of the FitzHugh-Nagumo System
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    El sistema FitzHugh-Nagumo tiene un tipo especial de solución llamada onda viajera, la cual tiene la forma u(x, t) = (x−μt) y w(x, t) = (x−μt), y es una solución estable en el tiempo. Nuestro interés es caracterizar numéricamente el perfil de una onda viajera (, ) y su velocidad de propagación μ(t). Con un cambio de variables, transformamos el problema de encontrar las soluciones en coordenadas originales a un problema de encontrar los equilibrios en un nuevo sistema de coordenadas llamado coordenadas móviles o sistema de coordenadas no locales. Con ejemplos numéricos demostraremos que las soluciones del sistema de EDPs en coordenadas no locales converge a una onda viajera del problema original. El sistema de coordenadas no locales también permite calcular la velocidad de propagación en forma exacta.

  • English

    The FitzHugh-Nagumo system has a special type of solution called traveling wave, which has the form u(x, t) = (x − μt) and w(x, t) = (x − μt), which is a stable solution over time. Our interest is to numerically characterize the profile of a traveling wave (, ) and its propagation speed μ(t). With achange of variables, we transform the problem of finding the solutions in original coordinates to a problem of finding the equilibria in a new coordinate system called mobile coordinates or non-local coordinatesystem. aa With numerical examples we will demonstrate that the solutions of the system of EDPs in non-local coordinates converge to a traveling wave of the original problem. The non-local coordinate system also allows to calculate the exact propagation speed.

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