Wright方程慢振荡周期解唯一性的研究进展
Recent advances about the uniqueness of the slowly oscillating periodic solutions of Wright's equation
摘要：
延迟方程中的一个古老猜想指出，Wright方程\[ y'(t)= - αy(t-1) [ 1+y(t)], α\in \mathbb{R} \]对于每个参数值$α>π/2$都有唯一的慢振荡周期解（SOPS）。我们重新制定这个猜想，我们使用一种方法称为验证继续严格计算的全球连续分支的SOPS赖特方程。使用这种方法，我们表明，该分支的一部分没有任何折叠点，也没有进行任何二次分叉，部分回答了新的重新表述的猜想。
英文摘要：
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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