Related papers: Generalized non-autonomous Cohen-Grossberg neural …
We investigate global bounded solutions of higher regularity to boundary value problems for a general linear nonautonomous first order 1D hyperbolic system in a strip. We establish the existence of such solutions under the assumption of…
This paper is concerned with establishing global asymptotic stability results for a class of non-linear PDE which have some similarity to the PDE of the Lifschitz-Slyozov-Wagner model. The method of proof does not involve a Lyapounov…
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…
In this paper, we establish the sufficient conditions guaranteeing global uniform exponential stability, or at least global asymptotic stability, of all solutions for nonlinear dynamical systems, also known as global incremental stability…
In this paper we study a nonlinear size-structured population model with distributed delay in the recruitment. The delayed problem is reduced into an abstract initial value problem of an ordinary differential equation in the Banach space by…
We consider a system of several nonlinear equations with a distributed delay and obtain absolute asymptotic stability conditions, independent of the delay. The ideas of the proofs are based on the notion of a strong attractor. The results…
We analyse and compare several algorithms to compute numerically periodic solutions of high-dimensional dynamical systems and investigate their Floquet stability without building the monodromy matrix. The solution and its perturbation are…
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…
The analysis of the long-term behavior of the mathematical model of a neural network constitutes a suitable framework to develop new tools for the dynamical description of nonautonomous state-dependent delay equations (SDDEs). The concept…
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.…
We consider the complex Ginzburg-Landau equation with two pure-power nonlinearities and a damping term. After proving a general global existence result, we focus on the existence and stability of several periodic orbits, namely the trivial…
We introduce a delay nonlinear differential equation model which describes how fish are harvested. In our previous studies we investigated the persistence of that equation and existence of a periodic solution for this equation. Here we…
In this paper we study a mixed problem for the nonlinear Schr\"odinger equation globally that have a nonlinear adding, in which the coefficient is a generalized function. Here is proved a global solvability theorem of the considered problem…
We study the asymptotic behavior of the solutions of the time-delayed higher-order dispersive nonlinear differential equation \begin{equation*} u_t(x,t)+Au(x,t) +\lambda_0(x) u(x,t)+\lambda(x) u(x,t-\tau )=0 \end{equation*} where…
Inspired by convolutional neural networks on 1D and 2D data, graph convolutional neural networks (GCNNs) have been developed for various learning tasks on graph data, and have shown superior performance on real-world datasets. Despite their…
We provide explicit conditions for uniform stability, global asymptotic stability and uniform exponential stability for dynamic equations with a single delay and a nonnegative coefficient. Some examples on nonstandard time scales are also…
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…
Systems with time delay play an important role in modeling of many physical and biological processes. In this paper we describe generic properties of systems with time delay, which are related to the appearance and stability of periodic…
We study the stability properties of linear time-varying systems in continuous time whose system matrix is Metzler with zero row sums. This class of systems arises naturally in the context of distributed decision problems, coordination and…