The slow wave solution to the FitzHugh-Nagumo equations

Abstract

This paper gives a new existence proof for a travelling wave solution to the FitzHugh-Nagumo equations, u_t = u_xx +f(u)−w, w _t = ∊ (u−γw). The proof uses a contraction mapping argument, and also shows that the solution (u, c, w) to the travelling wave equations, where c is the wave speed, converges as ∊ → 0⁺ to the solution to the equations having ∊=0, c=0, and w=0.

Keywords:

• Nerve conduction
• travelling waves
• threshold

AMS(MOS)::

• 35K57
• 34E10
• 34A34
• 92A90