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This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable and the set of admissible switching signals obeys pre-specified restrictions on switches between the subsystems and dwell times on…

Systems and Control · Electrical Eng. & Systems 2021-11-11 Atreyee Kundu

Various classes of stable finite difference schemes can be constructed to obtain a numerical solution. It is important to select among all stable schemes such a scheme that is optimal in terms of certain additional criteria. In this study,…

Numerical Analysis · Computer Science 2010-06-01 Petr N. Vabishchevich

This paper concerns some spectral properties of the scalar dynamical system defined by a linear delay-differential equation with two positive delays. More precisely, the existing links between the delays and the maximal multiplicity of the…

Dynamical Systems · Mathematics 2023-02-28 Sébastien Fueyo , Guilherme Mazanti , Islam Boussaada , Yacine Chitour , Silviu-Iulian Niculescu

This manuscript deals with the stability and bifurcation analysis of the equation $D^{2\alpha}x(t)+c D^{\alpha}x(t)=a x(t)+b x(t-\tau)$, where $0<\alpha<1$ and $\tau>0$. We sketch the boundaries of various stability regions in the parameter…

Dynamical Systems · Mathematics 2024-04-03 Sachin Bhalekar , Deepa Gupta

Delay differential equations (DDEs) with large delays play a pivotal role in understanding stability and bifurcations in systems ranging from neural networks to laser dynamics. While prior work has extensively studied DDEs with discrete…

Dynamical Systems · Mathematics 2025-09-09 Isam Al-Darabsah , Sue Ann Campbell , Bootan Rahman

In this paper, we consider the asymptotic stability for a system of linear delay differential equations. By analysing of the characteristic equation in detail, we have established the necessary and sufficient condition for the asymptotic…

Dynamical Systems · Mathematics 2025-04-03 Wataru Saito , Ikki Fukuda

Delays are ubiquitous in applied problems, but often do not arise as the simple constant discrete delays that analysts and numerical analysts like to treat. In this chapter we show how state-dependent delays arise naturally when modeling…

Dynamical Systems · Mathematics 2025-11-11 A. R. Humphries , A. S. Eremin , Z. Wang

Systems with time delay play an important role in modeling of many physical and biological processes. In this paper we describe generic properties of systems with time delay, which are related to the appearance and stability of periodic…

Chaotic Dynamics · Physics 2015-05-13 S. Yanchuk , P. Perlikowski

In this paper we characterise the global stability, global boundedness and recurrence of solutions of a scalar nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable autonomous…

Probability · Mathematics 2013-10-10 John A. D. Appleby , Jian Cheng , Alexandra Rodkina

This paper concerns the stability of analytical and numerical solutions of nonlinear stochastic delay differential equations (SDDEs). We derive sufficient conditions for the stability, contractivity and asymptotic contractivity in mean…

Numerical Analysis · Mathematics 2014-01-21 Siqing Gan , Aiguo Xiao , Desheng Wang

It is difficult to analyze the stability of systems with time-varying delays. One approach is to construct a time-transformation that converts the system into a form with a constant delay but with a time-varying scalar appearing in the…

Systems and Control · Electrical Eng. & Systems 2026-03-18 Jungbae Chun , Sengiyumva Kisole , Matthew M. Peet , Peter Seiler

This paper proposes a framework to assess the stability of an ordinary differential equation which is coupled to a 1D-partial differential equation (PDE). The stability theorem is based on a new result on Integral Quadratic Constraints…

Optimization and Control · Mathematics 2026-03-03 Matthieu Barreau , Carsten W. Scherer , Frederic Gouaisbaut , Alexandre Seuret

Long-term memory is a feature observed in systems ranging from neural networks to epidemiological models. The memory in such systems is usually modeled by the time delay. Furthermore, the nonlocal operators, such as the "fractional order…

Dynamical Systems · Mathematics 2023-05-12 Divya D. Joshi , Sachin Bhalekar , Prashant M. Gade

We describe a situation where an unstable equilibrium in a $3 \times 3$ system of linear differential equations may be stabilized by introducing a delayed response, i.e. converting to a system of delayed differential equations. This…

Dynamical Systems · Mathematics 2022-09-02 Alena Chan

This paper develops an explicit spectral representation for solutions of a one-dimensional linear wave equation with a constant time delay. The model is considered on a bounded interval with non-homogeneous Dirichlet boundary data and a…

Analysis of PDEs · Mathematics 2026-02-06 Javad A. Asadzade , Jasarat J. Gasimov , Nazim I. Mahmudov , Ismail T. Huseynov

New methods are developed for the stabilization of a linear system with general time-varying distributed delays existing at the system's states, inputs and outputs. In contrast to most existing literature where the function of time-varying…

Systems and Control · Electrical Eng. & Systems 2024-12-20 Qian Feng , Sing Kiong Nguang , Wilfrid Perruquetti

This paper deals with the stability analysis of a nonlinear time-delayed dispersive equation of order four. First, we prove the well-posedness of the system and give some regularity results. Then, we show that the zero solution of the…

Analysis of PDEs · Mathematics 2020-07-27 Kaïs Ammari , Boumediène Chentouf , Nejib Smaoui

In the present article, we discuss some aspects of the local stability analysis for a class of abstract functional differential equations. This is done under smoothness assumptions which are often satisfied in the presence of a…

Dynamical Systems · Mathematics 2015-02-12 Eugen Stumpf

We propose a system of partial differential equations with a single constant delay $\tau > 0$ describing the behavior of a one-dimensional thermoelastic solid occupying a bounded interval of $\mathbb{R}^{1}$. For an initial-boundary value…

Analysis of PDEs · Mathematics 2014-10-28 Denys Ya. Khusainov , Michael Pokojovy

In this paper, we investigate stability in distribution of neutral stochastic functional differential equations with infinite delay (NSFDEwID) at the state space \begin{equation*} C_{r}=\{{\varphi\in…

Probability · Mathematics 2021-05-25 Hussein K. Asker