Related papers: On solution manifolds for algebraic-delay systems
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…
A network of noisy bistable elements with global time-delayed couplings is considered. A dichotomous mean field model has recently been developed describing the collective dynamics in such systems with uniform time delays near the…
This paper deals with the exponential separation of type II, an important concept for random systems of differential equations with delay, introduced in \JM\ et al.~\cite{MiNoOb1}. Two different approaches to its existence are presented.…
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…
Time delay estimation plays a critical role in control, stabilization and state estimation of many practical system with time delay. In this paper, we propose a method to estimate delay for discrete time linear multiple-input…
We investigate the structure of the set of $T$-periodic solutions to periodically perturbed coupled delay differential equations on differentiable manifolds. By using fixed point index and degree-theoretic methods we prove the existence of…
A system of inhomogeneous second-order difference equations with linear parts given by noncommutative matrix coefficients are considered. Closed form of its solution is derived by means of newly defined delayed matrix sine/cosine using the…
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 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…
We consider port-Hamiltonian systems from a geometric perspective, where the quantities involved such as state, flows, and efforts evolve in (possibly infinite-dimensional) Banach spaces. The main contribution of this article is the…
A group classification of first-order delay ordinary differential equation (DODE) accompanied by an equation for delay parameter (delay relation) is presented. A subset of such systems (delay ordinary differential systems or DODSs) which…
This article is the third in a series the aim of which is to use Lie group theory to obtain exact analytic solutions of Delay Ordinary Differential Systems (DODSs). Such a system consists of two equations involving one independent variable…
The present paper deals with autonomous integral equations with infinite delay via dynamical system approach. Existence, local exponential attractivity, and other properties of center manifold are established by means of the…
Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed. Mathematical modeling of biological systems with delays is usually based on Delay Differential Equations (DDEs), a kind…
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…
In this paper, we study continuous and discrete linear delay systems given respectively by \[ \dot{X}(\xi) = A_0 X(\xi) + X(\xi)A_1 + B_0 X(\xi-\sigma) + X(\xi-\sigma)B_1 + G(\xi), \] and its discrete analogue \[ X(u+1) = A_0 X(u) + X(u)A_1…
We establish sufficient conditions for the existence and uniqueness of mean-field backward stochastic differential equations with time delayed generator in the sense that at t, the generator may depend on previous values up to a delay…
Real-world dynamical systems with retardation effects are described in general not by a single, precisely defined time delay, but by a range of delay times. An exact mapping onto a set of $N+1$ ordinary differential equations exists when…
The notion of delays arises naturally in many computational models, such as, in the design of circuits, control systems, and dataflow languages. In this work, we introduce \emph{automata with delay blocks} (ADBs), extending finite state…
We consider a delay differential equation (DDE) model for mode-locked operation in class-A semiconductor lasers containing both gain and absorber sections. The material processes are adiabatically eliminated as these are considered fast in…