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

Abstract

An old conjecture in delay equations states that Wright's equation y ′ ( t ) = − α y ( 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.