Unique wave front for dendritic spines with Nagumo dynamics

A model of dendritic spines uniformly distributed along a dendrite cable with the Nagumo dynamics for active membrane spine activity is considered. We show analytically the existence and uniqueness of traveling front solutions for a wide range of parameters including the spine density and the resistance between spine heads and dendrites. And such wave front travels at a slower speed for a larger spine density. Numerical simulations support the above results.