Related papers: Analytic Solution of a Delay Differential Equation…
We study the set of $T$-periodic solutions of a class of $T$-periodically perturbed Differential-Algebraic Equations, allowing the perturbation to contain a distributed and possibly infinite delay. Under suitable assumptions, the perturbed…
In the present paper, we consider a Cauchy problem for a linear second order in time abstract differential equation with pure delay. In the absence of delay, this problem, known as the harmonic oscillator, has a two-dimensional eigenspace…
Retarded stochastic differential equations (SDEs) constitute a large collection of systems arising in various real-life applications. Most of the existing results make crucial use of dissipative conditions. Dealing with "pure delay" systems…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
Hybrid numerical-experimental testing is a standard approach for complex dynamical structures that are, on the one hand, not easy to model due to complexity and parameter uncertainty and, on the other hand, too expensive for full-scale…
We present the linear-stability analysis of synchronised states in coupled time-delay systems. There exists a synchronisation threshold, for which we derive upper bounds, which does not depend on the delay time. We prove that at least for…
In this paper, we present estimates for solutions and for the attraction domain of the trivial solution for systems with delayed and nonlinear weighted homogeneous right-hand side of positive degree. The results are achieved via a…
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…
In this paper, by using the spectral theory of functions and properties of evolution semigroups, we establish conditions on the existence, and uniqueness of asymptotic 1-periodic solutions to a class of abstract differential equations with…
This contribution presents two exponential stability criteria for linear systems with multiple pointwise and distributed delays. These results (necessary and sufficient conditions) are given in terms of the delay Lyapunov matrix and the…
For linear periodic finite-dimensional systems, it is well-known that, first, exponential stability is equivalent to the existence of a unique periodic positive definite solution to the Lyapunov equation, and second, the Lyapunov equation…
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…
By developing new efficient techniques and using an appropriate fixed point theorem, we derive several new sufficient conditions for the pseudo almost periodic solutions with double measure for some system of differential equations with…
For two linear evolution differential equations systems - a normal ordinary differential equations system and a partial differential equations system with Stokes operator in a main part - with rapidly oscillating by time coefficients in a…
This work focuses on the well-posedness of McKean-Vlasov stochastic differential delay equations. Under suitable lipschitz conditions on the drift and diffusion terms, along with a distribution dependent Lyapunov condition, this paper shows…
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…
A simple non-autonomous scalar differential equation with delay, exponential decay, nonlinear negative feedback and a periodic multiplicative coefficient is considered. It is shown that stable slowly oscillating periodic solutions with the…
Using the principle of structural analogy of solutions, approaches have been developed for constructing exact solutions of complex nonlinear PDEs, including PDEs with delay, based on the use of special solutions to auxiliary simpler related…
An autonomous system of ordinary differential equations describing nonlinear oscillations on the plane is considered. The influence of time-dependent perturbations decaying at infinity in time is investigated. It is assumed that the…
This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…