Numerical Simulation of Traveling Waves of the FitzHugh-Nagumo System - Rubio-Mercedes, C.E. (2018)
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.