Description:
Several aspects of global dynamics and the existence of periodic solutions are studied for the scalar differential delay equation x'(t) = a(t)f(x([t-K])), where f(x) is a continuous negative feedback function, x f(x) < 0; x 6= 0, 0<a(t) is continuous w-periodic, [.] is the integer part function, and the integer K > 0 is the delay. The case of integer period w allows for a reduction to finite-dimensional difference equations. The dynamics of the latter are studied in terms of corresponding discrete maps, including the partial case of interval maps (K = 0).