Numerical Simulation of Traveling Waves of the FitzHugh-Nagumo System


  • C.E. Rubio-Mercedes UEMS-Universidade Estadual de Mato Grosso do Sul, Dourados, MS, Brasil
  • Glauce Barbosa Verao USP-Universidade de São Paulo, São Paulo, Brasil



Traveling wave, Stable solution, PDEs, Mobile coordinates


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 a
change 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 coordinate
system. 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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How to Cite

Rubio-Mercedes, C., & Barbosa Verao, G. (2018). Numerical Simulation of Traveling Waves of the FitzHugh-Nagumo System. Selecciones Matemáticas, 5(02), 193-203.