Related papers: Analytic Solution of a Delay Differential Equation…
The paper presents a numerical technique for computing directly the Takens-Bogdanov points in the nonlinear system of differential equations with one constant delay and two parameters. By representing the delay differential equations as…
Recently, we have studied a delay differential equation which has a coefficient that is a linear function of time. The equation has shown the oscillatory transient dynamics appear and disappear as the delay is increased between zero to…
We extend the definition of algebraic entropy to a class of differential-delay equations. The vanishing of the entropy, as a structural property of an equation, signals its integrability. We suggest a simple way to produce…
In this paper, we study the application of switched systems stability criteria to derive delay-dependent conditions for systems affected by both a constant and a time-varying delay. The main novelty of our approach lies on the use of…
We present a set of results concerning the existence of Lyapunov-Krasovskii functionals for classes of nonlinear switched systems with time-delay. In particular, we first present a result for positive systems that relaxes conditions…
Proportional delay is a particular case of time dependent delay. In this article, we consider differential equations involving multiple delays. The series solution of this equation leads to a class of special functions. This class of…
In this paper we give a necessary and suffcient conditions for the existence and uniqueness of periodic solutions of functional differential equations with n delay d dt x(t) = Ax(t) + n j=1 Bx(t -- r j) + f (t). The conditions are obtained…
A wide class of non-autonomous nonlinear parabolic partial differential equations with delay is studied. We allow in our investigations different types of delays such as constant, time-dependent, state-dependent (both discrete and…
Motivated by Lazer-Leach type results, we study the existence of periodic solutions for systems of functional-differential equations at resonance with an arbitrary even-dimensional kernel and linear deviating terms involving a general delay…
The main purpose of this paper is to provide a summary of the fundamental methods for analyzing delay differential equations arising in biology and medicine. These methods are employed to illustrate the effects of time delay on the behavior…
This paper investigates the problem of solving discrete-time Lyapunov equations (DTLE) over a multi-agent system, where every agent has access to its local information and communicates with its neighbors. To obtain a solution to DTLE, a…
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…
In this note, we study distributed time-varying optimization for a multi-agent system. We first focus on a class of time-varying quadratic cost functions, and develop a new distributed algorithm that integrates an average estimator and an…
We establish conditions guaranteeing that all eventually positive increasing solutions of a half-linear delay differential equation are regularly varying and derive precise asymptotic formulae for them. The results here presented are new…
Dissipative estimator (observer) design for continuous time-delay systems poses a significant challenge when an unlimited number of pointwise and general distributed delays (DDs) are concerned. We propose an effective solution to this…
The solvability and stability analysis of linear time invariant systems of delay differential-algebraic equations (DDAEs) is analyzed. The behavior approach is applied to DDAEs in order to establish characterizations of their solvability in…
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…
In this paper we consider a boundary value problem for fully fourth order nonlinear functional differential equation which contains all lower derivatives of proportional delay arguments. By the reduction of the problem to operator equation…
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…
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…