  The use of high-frequency currents in neurostimulation has received increased
attention in recent years due to its varied effects on tissues and cells.
Neurons are commonly modeled as nonlinear systems, and questions such as
stability can thus be addressed with well-known averaging methods. A recent
strategy called interferential currents uses electrodes delivering sinusoidal
signals of slightly different frequencies, and thus classical averaging
(well-adapted to deal with a single frequency) cannot be directly applied. In
this paper, we consider the one-dimensional FitzHugh-Nagumo system under the
effects of a source composed of two terms that are sinusoidal in time and
quadratically decaying in space. To study this setting we develop a new
averaging strategy to prove that, when the frequencies involved are
sufficiently high, the full system can be approximated by an explicit
highly-oscillatory term plus the solution of a simpler -- albeit non-autonomous
-- system. This decomposition can be seen as a stability result around a
varying trajectory. One of the main novelties of the proofs presented here is
an extension of the contracting rectangles method to the case of parabolic
equations with space and time-depending coefficients.
