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arXiv · 0909.4107

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

Jean-Philippe Lessard
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Abstract

An old conjecture in delay equations states that Wright's equation \[ y'(t)= - αy(t-1) [ 1+y(t)], α\in \mathbb{R} \] 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 nor does it undergo any secondary bifurcation, partially answering the new reformulated conjecture.

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Jean-Philippe Lessard. 2009-09-24. Recent advances about the uniqueness of the slowly oscillating periodic solutions of Wright's equation. https://arxiv.org/abs/0909.4107

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