Discrete impulses in ephaptically coupled nerve fibers

We exclusively analyze the condition for modulated waves to emerge in two ephaptically coupled nerve fibers. Through the multiple scale expansion, it is shown that a set of coupled cable-like Hodgkin-Huxley equations can be reduced to a single differential-difference nonlinear equation. The standard approach of linear stability analysis of a plane wave is used to predict regions of parameters where nonlinear structures can be observed. Instability features are shown to be importantly controlled not only by the ephaptic coupling parameter, but also by the discreteness parameter. Numerical simulations, to verify our analytical predictions, are performed, and we explore the longtime dynamics of slightly perturbed plane waves in the coupled nerve fibers. On initially exciting only one fiber, quasi-perfect interneuronal communication is discussed along with the possibility of recruiting damaged or non-myelinated nerve fibers, by myelinated ones, into conduction.