Related papers: Characteristic matrix functions for delay differen…

We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…

In this note, we discuss a generalization of the well-known implicit function theorem to the time-delay case. We show that the latter problem is closely related to the bicausal changes of coordinates of time-delay systems. An iterative…

Networks of neural mass nodes with delayed interactions are increasingly being used as models for large-scale brain activity. To complement the growing number of computational studies of such networks, it is timely to develop new…

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…

In this paper we consider an interior stabilization problem for the wave equation with dynamic boundary delay.We prove some stability results under the choice of damping operator. The proof of the main result is based on a frequency domain…

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…

In this work, we consider the regularity property of stochastic convolutions for a class of abstract linear stochastic retarded functional differential equations with unbounded operator coefficients. We first establish some useful estimates…

We propose a delayed Mittag-Leffler type matrix function with logarithm, which is an extension of the classical Mittag-Leffler type matrix function with logarithm and delayed Mittag-Leffler type matrix function. With the help of the delayed…

Stability of retarded differential equations is closely related to the existence of Lyapunov-Krasovskii functionals. Even if a number of converse results have been reported regarding the existence of such functionals, there is a lack of…

The linear nonhomogeneous fractional difference system with constant coefficients is introduced. An explicit solution to the system is acquired by proposing a newly discrete retarded perturbation of the nabla Mittag-Leffer-type function…

Eigenstate phases such as the discrete time crystal exhibit an inherent instability upon the coupling to an environment, which restores equipartition of energy and therefore acts against the protecting nonergodicity. Here, we demonstrate…

The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge of instability, i.e. a pair of roots of the characteristic…

In this study, we introduce and explore a delay differential equation that lends itself to explicit solutions in the Fourier-transformed space. Through the careful alignment of the initial function, we can construct a highly accurate…

We introduce a class of doubly infinite complex Jacobi matrices determined by a simple convergence condition imposed on the diagonal and off-diagonal sequences. For each Jacobi matrix belonging to this class, an analytic function, called a…

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…

In this article we study networks of coupled dynamical systems with time-delayed connections. If two such networks hold different delays on the connections it is in general possible that they exhibit different dynamical behavior as well. We…

In this paper we study the stabilization of rotating waves using time delayed feedback control. It is our aim to put some recent results in a broader context by discussing two different methods to determine the stability of the target…

We study the existence of a periodic solution for a differential equation with distributed delay. It is shown that, for a class of distributed delay diferential quations, a symmetric period 2 solution, where the period is twice the maximum…

Many dynamic processes involve time delays, thus their dynamics are governed by delay differential equations (DDEs). Studying the stability of dynamic systems is critical, but analyzing the stability of time-delay systems is challenging…

This paper deals with the boundary stabilization problem of a one-dimensional wave equation with a switching time-delay in the boundary. We show that the problem is well-posed in the sense of semigroups theory of linear operators. Then, we…