  The classical biophysical Morris-Lecar model of neuronal excitability
predicts that upon stimulation of the neuron with a sufficiently large constant
depolarizing current there exists a finite interval of the current values where
periodic spike generation occurs. Above the upper boundary of this interval,
there is four-stage damping of the spike amplitude: 1) minor primary damping,
which reflects a typical transient to stationary dynamic state, 2) plateau of
nearly undamped periodic oscillations, 3) strong damping, and 4) reaching a
constant asymptotic value of the neuron potential. We have shown that in the
vicinity of the asymptote the Morris-Lecar equations can be reduced to the
standard equation for exponentially damped harmonic oscillations. Importantly,
all coefficients of this equation can be explicitly expressed through
parameters of the original Morris-Lecar model, enabling direct comparison of
the numerical and analytical solutions for the neuron potential dynamics at
later stages of the spike amplitude damping.
