Change of the attractor structure for when f changes from monotone to non-monotone negative feedback

It is known that for bounded f with monotone negative feedback, the scalar delay equation has an attractor A (within the slowly oscillating solution class) that is a two-dimensional graph. A slowly oscillating periodic orbit divides the surface A into an interior part containing zero and an exterior part. We describe deformations of f to functions with non-monotone negative feedback which preserve the interior part, but make orbits from the exterior part converge to zero as t→∞. Thus, the graph structure of A is lost in such deformations of f.