abstr16

It is known that for bounded  f with monotone negative feedback,  the scalar delay equation
 x'(t) = f(x(t-1))  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   goes to infinity.
Thus,  the graph structure of A is lost in such deformations of    f.

 Back to homepage