The equation x'(t) = - µ x(t) + f(x(t-1)) , with µ #> 0 and xf(x) #< 0 for #= x *E R, is a prototype for delayed negative feedback combined with friction. Its semiflow on C = C([-1,0],R) leaves a set S invariant, which also plays a major role for the dynamics on the full space C . The main result determines the attractor of the semiflow restricted to the closure of S for monotone, bounded, smooth f. In the course of the proof, Walther derives Poincaré-Bendixson theorems for differential-delay equations. The method used here is unique in its use of winding numbers and homotopies in nonconvex sets.
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