Recent advances about the uniqueness of the slowly oscillating periodic solutions of Wright’s equation

An old conjecture in delay equations states that Wright’s equation y(t) = −αy(t− 1)[1 + y(t)], α ∈ R has a unique slowly oscillating periodic solution (SOPS) for every parameter value α > π/2. We reformulate this conjecture and we use a method called validated continuation to rigorously compute a global continuous branch of SOPS of Wright’s equation. Using this method, we show that a part of this branch does not have any fold point, partially answering the new reformulated conjecture.