The Pantelides algorithm for delay differential-algebraic equations

Effects of Roots of Maximal Multiplicity on the Stability of Some Classes of Delay Differential-Algebraic Systems: The Lossless Propagation Case

It has been observed in several recent works that, for some classes of linear time-delay systems, spectral values of maximal multiplicity are dominant, a property known as multiplicity-induced-dominancy (MID). This paper starts the investigation of whether MID holds for delay differential-algebraic systems by considering a single-delay system composed of two scalar equations. After motivating this problem and recalling some recent results for retarded delay differential equations, we prove that the MID property holds for the delay differential-algebraic system of interest and present some appl…

Delay differential-algebraic equations in real-time dynamic substructuring

Hybrid numerical-experimental testing is a standard approach for complex dynamical structures that are, on the one hand, not easy to model due to complexity and parameter uncertainty and, on the other hand, too expensive for full-scale experiments. The main idea is to subdivide the structure in a part that can be accurately simulated with numerical methods and an experimental component. The numerical simulation and the experiment are coupled in real-time by a so-called transfer system, which induces a time-delay into the system. In this paper, we study the solvability of the resulting hybrid n…

将状态依赖时滞微分方程中的周期轨道作为代数方程的根进行求解

Finding periodic orbits in state-dependent delay differential equations as roots of algebraic equations

本研究证明时滞微分方程周期边值问题局部等价于有限维代数方程组，将该结论应用于状态依赖时滞微分方程，给出其Hopf分岔定理的初等证明，拓展了原有相关理论成果。

On a class of differential-algebraic equations with infinite delay

We study the set of $T$-periodic solutions of a class of $T$-periodically perturbed Differential-Algebraic Equations, allowing the perturbation to contain a distributed and possibly infinite delay. Under suitable assumptions, the perturbed equations are equivalent to Retarded Functional (Ordinary) Differential Equations on a manifold. Our study is based on known results about the latter class of equations.

线性时不变随机延迟微分方程二阶矩稳定边界的代数条件

Algebraic conditions for second-moment stability boundaries of linear, time-invariant stochastic delay-differential equations

针对带乘性和加性噪声的线性时不变随机延迟微分方程，推导出无需离散化的半解析代数等式条件，用于确定二阶矩稳定边界，并通过低维模型验证其有效性。

Stability of traveling wavefronts in discrete reaction-diffusion equations with nonlocal delay effects

This paper deals with traveling wavefronts for temporally delayed, spatially discrete reaction-diffusion equations. Using a combination of the weighted energy method and the Green function technique, we prove that all noncritical wavefronts are globally exponentially stable, and critical wavefronts are globally algebraically stable when the initial perturbations around the wavefront decay to zero exponentially near minus infinity regardless of the magnitude of time delay.

A Core Theory of Delay Systems

We introduce a framework for the description of a large class of delay-differential algebraic systems, in which we study three core problems: first we characterize abstractly the well-posedness of the initial-value problem, then we design a practical test for well-posedness based on a graph-theoretic representation of the system; finally, we provide a general stability criterion. We apply each of these results to a structure that commonly arises in the control of delay systems.

带分布时滞的线性差分时滞方程的$L^q$近似能控性频率判据

$L^q$ approximate controllability frequency criterion for linear difference delay equations with distributed delays

该研究基于代数视角与Y. Yamamoto的实现理论，提出带分布时滞的线性差分时滞方程有限时间$L^q$近似能控性的频域充要判据，并得到其最小能控时间的上界。

On the computation of the term $w_{21}z^2\bar{z}$ of the series defining the center manifold for a scalar delay differential equation

In computing the third order terms of the series of powers of the center manifold at an equilibrium point of a scalar delay differential equation, with a single constant delay $r>0,$ some problems occur at the term $w_{21}z^2\bar{z}.$ More precisely, in order to determine the values at 0, respectively $-r$ of the function $w_{21}(\,.\,),$ an algebraic system of equations must be solved. We show that the two equations are dependent, hence the system has an infinity of solutions. Then we show how we can overcome this lack of uniqueness and provide a formula for $w_{21}(0).$

关于具有更一般状态依赖时滞的某些微分方程的解流形

On solution manifolds of some differential equations with more general state-dependent delay

本文针对具有状态依赖时滞的微分方程，提出一种新证明，表明其解流形与特定子空间开子集微分同胚，无需依赖先前关于时滞形式的限制性假设，并采用algebraic-delay systems框架。

Models for plasma kinetics during simultaneous therapeutic plasma exchange and extracorporeal membrane oxygenation

This paper focuses on the derivation and simulation of mathematical models describing new plasma fraction in blood for patients undergoing simultaneous extracorporeal membrane oxygenation and therapeutic plasma exchange. Models for plasma exchange with either veno-arterial or veno-venous extracorporeal membrane oxygenation are considered. Two classes of models are derived for each case, one in the form of an algebraic delay equation and another in the form of a system of delay differential equations. In special cases, our models reduce to single compartment ones for plasma exchange that have b…

Periodic Solutions of a Singularly Perturbed Delay Differential Equation With Two State-Dependent Delays

Periodic orbits and associated bifurcations of singularly perturbed state-dependent delay differential equations (DDEs) are studied when the profiles of the periodic orbits contain jump discontinuities in the singular limit. A definition of singular solution is introduced which is based on a continuous parametrisation of the possibly discontinuous limiting solution. This reduces the construction of the limiting profiles to an algebraic problem. A model two state-dependent delay differential equation is studied in detail and periodic singular solutions are constructed with one and two local max…

分布式延迟微分方程中记忆诱导的爆破解及其动力学转变

Memory-induced blow-up solutions and their dynamical transitions in distributed delay differential equations

本文研究分布式延迟微分方程中记忆效应诱导的有限时间爆破，通过线性链技巧约化为二维ODE并分析无穷远动力学，发现记忆可加速爆破速率或转变爆破类型，且存在阈值现象控制爆破发生。

解流形简化的直接方法

A direct approach to simplicity of solution manifolds

本文提出了一种直接方法，通过构造微分同胚将解流形映射到由ϕ'(0)=0定义的子空间，从而简化了解流形的分析过程。