Study of propagation along nonuniform excitable fibers

Two related reaction diffusion systems that support traveling wave solutions when parameters are constant are studied when there are jump discontinuities in the diffusion coefficient. The first system represents a classical axon model where the fiber had a jump in diameter at discrete locations and the membrane dynamics represent those of barnacle muscle (which we call Morris-Lecar dynamics). The second model represents a passive cable with a uniform density of spines that have Morris-Lecar dynamics. Conditions under which echo waves form are studied, as well as conditions when wave blocking takes place with a thickening of the fiber.