  This paper predicts the ability to externally control the firing times of a
cortical neuron whose behavior follows the Izhikevich neuron model. The
Izhikevich neuron model provides an efficient and biologically plausible method
to track a cortical neuron's membrane potential and its firing times. The
external control is a simple optogenetic model represented by an illumination
source that stimulates a saturating or decaying membrane current. This paper
considers firing frequencies that are sufficiently low for the membrane
potential to return to its resting potential after it fires. The time required
for the neuron to charge and for the neuron to recover to the resting potential
are numerically fitted to functions of the Izhikevich neuron model parameters
and the peak input current. Results show that simple functions of the model
parameters and maximum input current can be used to predict the charging and
recovery times, even when there are deviations in the actual parameter values.
Furthermore, the predictions lead to lower bounds on the firing frequency that
can be achieved without significant distortion.
