Figure 2.

An example of a numerical solution of Equation 39 showing non-linear evolution of a_k(t) as a function of t (top) and an expanded view of a single spike (bottom) using ${\beta }_k^{\prime }=exp(i\pi /4)$, β_k = 2 exp(−iπ/4), α_k = 3, and γ_k = 1.996 + i. The solution shows behavior in close agreement with typical axonal spiking but is derived directly from first principles of electrodynamics and wave propagation without any reference to the standard ad hoc reaction-diffusion approach of HH.