Topics in Delay Differential Equations

Hans-Otto Walther

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Topics in Delay Differential Equations

机译：时滞微分方程主题

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摘要

We introduce delay differential equations, give some motivation by applications, review basic facts about initial value problems from wellposedness to the variation-of-constants formula in the sun-star-framework, and discuss two topics in greater detail: (a) The dynamics generated by autonomous scalar equations with a single, constant time lag, from existence of periodic solutions to the fine structure of global attractors and chaotic motion, and (b) more recent results on equations with state-dependent delay (lack of smoothness, differentiable solution operators on suitable Banach manifolds, case studies). The final part addresses directions of future research.

机译：我们介绍了延迟微分方程，给出了一些应用动机，复习了有关太阳星框架中从适定性到常数变化公式的初值问题的基本事实，并更详细地讨论了两个主题：（a）动力学由具有单个恒定时滞的自治标量方程生成，从周期解的存在到全局吸引子的精细结构和混沌运动，以及（b）具有状态相关延迟（缺乏光滑度，可微解）的方程的最新结果合适的Banach流形上的操作员，案例研究）。最后一部分介绍了未来研究的方向。

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来源
《Jahresbericht der Deutschen Mathematiker-Vereinigung》 |2014年第2期|87-114|共28页
作者
Hans-Otto Walther;
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作者单位

Mathematisches Institut, Universitaet Giessen, Arndtstr. 2, 35392 Giessen, Germany;

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正文语种 eng
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关键词
Delay differential equation; Characteristic equation; Infinite-dimensional dynamical system; Semiflow; Periodic orbit; Bifurcation; Floquet multiplier; Global attractor; Morse-Smale decomposition; Hyperbolic set; Chaos; State-dependent delay; Solution manifold;

机译：时滞微分方程;特征方程;无限维动力系统;半流周期性轨道分叉;浮球乘法器;全球吸引者Morse-Smale分解;双曲集;混沌;与国家有关的延迟;溶液歧管;

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Topics in Delay Differential Equations

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