Effect of high-frequency stimulation on nerve pulse propagation in the FitzHugh-Nagumo model

We consider the FitzHugh-Nagumo model axon under action of a homogeneous high-frequency stimulation (HFS) current. Using a multiple scale method and a geometrical singular perturbation theory, we derive analytically the main characteristics of the traveling pulse. We show that the effect of HFS on the axon is determined by a parameter proportional to the ratio of the amplitude to the frequency of the stimulation current. When this parameter is increased, the pulse slows down and shrinks. At some threshold value, the pulse stops and its width becomes zero. The HFS prevents the pulse propagation when the parameter exceeds the threshold value. The analytical results are confirmed by numerical experiments performed with the original system of partial differential equations.