Uniqueness of Slowly Oscillating Periodic Solutions

This paper discusses the slowly oscillating periodic solutions of the negative feedback differential delay equation ẏ(t) = − λy(t) + λf(y(t − 1)), where ƒ(y) is an odd function and λ > 0 is a parameter. Using the Inclination Lemma, we show that, for all large λ, the slowly oscillating periodic solutions form a one-parameter family as the bifurcations of a heteroclinic orbit of the equation ẋ(t) = γx(t) + γf(x(t − 1)) (γ > 0).