Continuous dependence of rotation numbers for model family of piecewise continuous one-dimensional maps

We consider a piecewise monotonic, piecewise continuous maps the real line, simulating the dynamics of some neural and telecommunications networks. For maps of the classes nonwandering set is the disjoint union of the sets of nonwandering two maps of Lorenz type. Thus, we can define the rotation rotation of the studied maps. It is proved that there are a lot of rotation the union of two closed intervals, the boundary points are continuously depend on the maps (with the Hausdorff topology).