  We develop two iteration schemes for construction of localized stationary
solutions (bumps) of a one-population Wilson-Cowan model with a smoothed
Heaviside firing rate function. The first scheme is based on the fixed point
formulation of the stationary Wilson-Cowan model. The second one is formulated
in terms of the excitation width of a bump. Using the theory of monotone
operators in ordered Banach spaces we justify convergence of both iteration
schemes.
