论文标题
对称单调反馈的延迟方程中周期性解决方案的全局分叉
Global Bifurcation of Periodic Solutions in Delay Equations with Symmetric Monotone Feedback
论文作者
论文摘要
我们研究了延迟方程的周期性解决方案$ \ dot {x}（t）= f（x（t），x（t-1））$，其中$ f $ starcor在延迟组件中严格单调，并且具有均匀的odd对称性。我们通过源自平面普通微分方程的周期图，完全描述了周期性解决方案的全球分叉结构。此外，我们证明了时期图的第一个衍生物决定了周期轨道的局部稳定性。本文以卡普兰和约克的开创性工作为基础，后者找到了一些与偶数对称的对称的周期性解决方案。我们通过证明所有周期性解决方案是对称的，如果$ f $是另外单调，我们可以增强他们的结果。
We study the periodic solutions of the delay equation $\dot{x}(t)=f(x(t),x(t-1))$, where $f$ scalar is strictly monotone in the delayed component and has even-odd symmetry. We completely describe the global bifurcation structure of periodic solutions via a period map originating from planar ordinary differential equations. Moreover, we prove that the first derivative of the period map determines the local stability of the periodic orbits. This article builds on the pioneering work of Kaplan and Yorke, who found some symmetric periodic solutions for $f$ with even-odd symmetry. We enhance their results by proving that all periodic solutions are symmetric if $f$ is in addition monotone.
