Related papers: Oscillation results for first order neutral delay …
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…
We present new explicit exponential stability conditions for the linear scalar neutral equation with two variable coefficients and delays $$ (x(t)-a(t)x(g(t)))'=-b(t)x(h(t)), $$ where $|a(t)|<1$, $b(t)\geq 0$, $h(t)\leq t$, $g(t)\leq t$, in…
We obtain new explicit exponential stability conditions for the linear scalar neutral equation with two bounded delays $ \dot{x}(t)-a(t)\dot{x}(g(t))+b(t)x(h(t))=0, $ where $ 0\leq a(t)\leq A_0<1$, $0<b_0\leq b(t)\leq B$, using the…
Spectral properties and transition to instability in neutral delay differential equations are investigated in the limit of large delay. An approximation of the upper boundary of stability is found and compared to an analytically derived…
We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…
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 discuss the occurrence of oscillatory solutions which decay to 0 as $s\to+\infty$ for a class of perturbed second order ordinary differential equations. As opposed to other results in the recent literature, the perturbation is as small…
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 have considered higher order two dimensional coupled system of non-linear ordinary differential equations. We have given necessary and sufficient conditions on the non-linear functions such that the solutions pair oscilla
For the delay differential equations $$ \ddot{x}(t) +a(t)\dot{x}(g(t))+b(t)x(h(t))=0, g(t)\leq t, h(t)\leq t, $$ and $$ \ddot{x}(t) +a(t)\dot{x}(t)+b(t)x(t)+a_1(t)\dot{x}(g(t))+b_1(t)x(h(t))=0 $$ explicit exponential stability conditions…
The Riccati equation method is used for study the oscillatory and non oscillatory behavior of solutions of systems of two first order linear two by two dimensional matrix differential equations. An integral and an interval oscillatory…
In this paper, we discuss the method of obtaining symmetries for second order nonhomogeneous neutral differential equations with variable coefficients. We use Taylor theorem for a function of several variables to obtain a Lie type…
This paper extends the discriminant associated to second order linear constant coefficient differential equations to general second order linear differential equations. The main result of this paper is that the discriminant of a second…
This paper analyzes the eigenvalue distribution of neutral differential systems and the corresponding difference systems, and establishes the relationship between the eigenvalue distribution and delay-independent stability of neutral…
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…
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 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…
The Riccati equation method is used to establish new oscillation criteria for extended linear matrix Hamiltonian systems. This method allows to obtain results in in a new direction, which is to break the positive definiteness condition,…
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 describe an algorithm for the numerical solution of second order linear differential equations in the highly-oscillatory regime. It is founded on the recent observation that the solutions of equations of this type can be accurately…