Diffusion dependence of the FitzHugh-Nagumo equations

Abstract:

We investigate the behavior of the solutions of \[ \begin {array}{*{20}{c}} {{u_t} = {u_{x x}} - \alpha u - v + f(u),} \\ {{v_t} = \eta {v_{x x}} + \sigma u - \gamma v,} \\ \end {array} \] as $\eta$ tends to zero from above.