Related papers: On stability of linear neutral differential equati…
This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…
For the nonlinear second order Lienard-type equations with time-varying delays $$ \ddot{x}(t)+\sum_{k=1}^m f_k(t,x(t),\dot{x}(g_k(t)))+\sum_{k=1}^l s_k(t,x(h_k(t)))=0, $$ global asymptotic stability conditions are obtained. The results are…
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…
Analysis of the systems involving delay is a popular topic among applied scientists. In the present work, we analyze the generalized equation $D^{\alpha} x(t) = g\left(x(t-\tau_1), x(t-\tau_2)\right)$ involving two delays viz. $\tau_1\geq…
A nonlinear stochastic differential equation with the order of nonlinearity higher than one, with several discrete and distributed delays and time varying coefficients is considered. It is shown that the sufficient conditions for…
The problem considered in the paper is exponential stability of linear equations and global attractivity of nonlinear non-autonomous equations which include a non-delay term and one or more delayed terms. First, we demonstrate that…
This paper considers linear functional equations on $\mathbb R^d$ with distributed delays defined by matrix-valued measures of bounded variation. More precisely, we are interested in providing conditions to ensure that the exponential…
Various results and techniques, such as Bohl-Perron theorem, a priori solution estimates, M-matrices and the matrix measure, are applied to obtain new explicit exponential stability conditions for the system of vector functional…
This paper deals with the stability of linear periodic difference delay systems, where the value at time $t$ of a solution is a linear combination with periodic coefficients of its values at finitely many delayed instants…
In this paper, we study asymptotic stability of the zero solution of a class of differential systems governed by a scalar differential inequality with time-varying structures and delays. We establish a new generalized Halanay inequality for…
While the asymptotic stability of positive linear systems in the presence of bounded time delays has been thoroughly investigated, the theory for nonlinear positive systems is considerably less well-developed. This paper presents a set of…
There is a close connection between stability and oscillation of delay differential equations. For the first-order equation $$ x^{\prime}(t)+c(t)x(\tau(t))=0,~~t\geq 0, $$ where $c$ is locally integrable of any sign, $\tau(t)\leq t$ is…
For a mixed (advanced--delay) differential equation with variable delays and coefficients $$ \dot{x}(t) \pm a(t)x(g(t)) \mp b(t)x(h(t)) = 0, t\geq t_0 $$ where $$ a(t)\geq 0, b(t)\geq 0, g(t)\leq t, h(t)\geq t $$ explicit nonoscillation…
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…
Suppose any solution of a linear impulsive delay differential equation $$ \dot{x} (t) + \sum_{i=1}^m A_i (t) x[h_i (t)] = 0,~t \geq 0, x(s) = 0, s < 0, $$ $$ x(\tau_j +0) = B_j x(\tau_j -0) + \alpha_j, ~j=1,2, ... ,$$ is bounded for any…
In this paper, we introduce the notion of boundary delay equations, establishing a unified framework for analyzing linear time-invariant systems with pure time-delayed boundary conditions. We establish mild sufficient conditions for the…
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 consider a linear scalar delay differential equation (DDE), consisting of two arbitrary distributed time delays. We formulate necessary conditions for stability of the trivial solution which are independent of the distributions. For the…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
In this paper, we present sufficient conditions for asymptotic stability and exponential stability of a class of impulsive neutral differential equations with discrete and distributed delays. Our approaches are based on the method using…