More About the Math:
The Traveling Spike (Part 1)
Of course, a spike would not be much of much use if it was just generated
in one neuron and never went anywhere.
In the brain, spikes travel down
long cables of nerve cell called axon to influence other downstream neurons
or to cause muscle cells far away from the brain to contract. Although there
are many additional biophysical tricks, the fundamental mechanism can be
understood from the Hodgkin and Huxley equations.
Here is a spatially extended neuron:
From Johnston and Wu, Foundations of Cellular Neurophysiology, MIT Press, 1997. Figure from p.2.
CLICK HERE to see how mathematics describes this traveling spike.