Related papers: Analyzing stability of a delay differential equati…
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…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
Stability analysis is performed for a linear differential equation with two delays. Geometric arguments show that when the two delays are rationally dependent, then the region of stability increases. When the ratio has the form 1/n, this…
Time lags occur in a vast range of real-world dynamical systems due to finite reaction times or propagation speeds. Here we derive an analytical approach to determine the asymptotic stability of synchronous states in networks of coupled…
A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be…
Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…
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…
This paper studies how complicated and irregular behavior, known as chaos, can arise in a simple mathematical model that includes time delays. The model is a delay differential equation in which the present rate of change depends not only…
The dynamics of the delay logistic equation with complex parameters and arbitrary complex initial conditions is investigated. The analysis of the local stability of this difference equation has been carried out. We further exhibit several…
Stability of linear systems with uncertain bounded time-varying delays is studied under assumption that the nominal delay values are not equal to zero. An input-output approach to stability of such systems is known to be based on the bound…
Time delays are a common perturbation in systems with many states, such as networked, distributed, or decentralized systems. Current methods analyzing the stability of large systems with time delay typically produce very conservative…
We study the stability of general $n$-dimensional nonautonomous linear differential equations with infinite delays. Delay independent criteria, as well as criteria depending on the size of some finite delays are established. In the first…
In our manuscript, we develop a new approach for stability analysis of one-dimensional wave equation with time delay. The major contribution of our work is to develop a new method for spectral analysis. We derive sufficient and necessary…
Dynamical networks with time delays can pose a considerable challenge for mathematical analysis. Here, we extend the approach of generalized modeling to investigate the stability of large networks of delay-coupled delay oscillators. When…
We consider delay differential equations with a polynomially distributed delay. We derive an equivalent system of delay differential equations, which includes just two discrete delays. The stability of the equivalent system and its…
Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote…
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…
We introduce the map representation of a time-delayed system in the presence of delay time modulation. Based on this representation, we find the method by which to analyze the stability of that kind of a system. We apply this method to a…
This work deals with a scalar nonlinear neutral delay differential equation issued from the study of wave propagation. A critical value of the coefficients is considered, where only few results are known. The difficulty follows from the…
In this paper we analyze a coupled system between a transport equation and an ordinary differential equation with time delay (which is a simplified version of a model for kidney blood flow control). Through a careful spectral analysis we…