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

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

2009-09-22

arxiv.org/abs/0909.4107v2

Mathematics

Dynamical Systems

25 pages, 4 figures

Scientific paper

An old conjecture in delay equations states that Wright's equation \[ y'(t)= - \alpha y(t-1) [ 1+y(t)], \alpha \in \mathbb{R} \] has a unique slowly oscillating periodic solution (SOPS) for every parameter value $\alpha>\pi/2$. 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 nor does it undergo any secondary bifurcation, partially answering the new reformulated conjecture.

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