相关论文: Asymptotic behavior of solutions to linear evoluti…

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…

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 obtain conditions for existence of unique global or maximally extended solutions to generalized neural field equations. We also study continuous dependence of these solutions on the spatiotemporal integration kernel, delay effects,…

We study abstract linear and nonlinear evolutionary systems with single or multiple delay feedbacks, illustrated by several concrete examples. In particular, we assume that the operator associated with the undelayed part of the system…

The Kuramoto model is a system of ordinary differential equations for describing synchronization phenomena defined as a coupled phase oscillators. In this paper, a bifurcation structure of the infinite dimensional Kuramoto model is…

Functional evolution equations are used in the modeling of numerous physical processes. In this work, our main tool is perturbation theory of strongly continuous semigroups. The advantage of this technique is that one can provide functional…

Delay differential equations (DDEs) with large delays play a pivotal role in understanding stability and bifurcations in systems ranging from neural networks to laser dynamics. While prior work has extensively studied DDEs with discrete…

In this work, spectrum and asymptotics of eigenfunctions of a generalized class of boundary value problems with a delay are obtained.

We prove that the spectrum of the linear delay differential equation $x'(t)=A_{0}x(t)+A_{1}x(t-\tau_{1})+\ldots+A_{n}x(t-\tau_{n})$ with multiple hierarchical large delays $1\ll\tau_{1}\ll\tau_{2}\ll\ldots\ll\tau_{n}$ splits into two…

We investigate the effects of a time-delayed all-to-all coupling scheme in a large population of oscillators with natural frequencies following a bimodal distribution. The regions of parameter space corresponding to synchronized and…

In this note, we analyze an abstract evolution equation with time-dependent time delay and time-dependent delay feedback coefficient. We assume that the operator corresponding to the nondelayed part of the model generates an exponentially…

In the present paper we investigate the influence of the retarded access by a time-varying delay on the dynamics of delay systems. We show that there are two universality classes of delays, which lead to fundamental differences in dynamical…

In this paper, we investigate the global exponential stability for complex-valued recurrent neural networks with asynchronous time delays by decomposing complex-valued networks to real and imaginary parts and construct an equivalent…

In this paper, time delay effect and distributed shear are considered in the Kuramoto model. On the Ott-Antonsen's manifold, through analyzing the associated characteristic equation of the reduced functional differential equation, the…

We consider the problem of discretizing evolution operators of linear delay equations with the aim of approximating their spectra, which is useful in investigating the stability properties of (nonlinear) equations via the principle of…

In order to discover generic effects of heterogeneous communication delays on the dynamics of large systems of coupled oscillators, this paper studies a modification of the Kuramoto model incorporating a distribution of interaction delays.…

We apply a recently proposed method for the analysis of time series from systems with delayed feedback to experimental data generated by a CO_2 laser. The method is able to estimate the delay time with an error of the order of the sampling…

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 consider abstract evolution equations with on-off time delay feedback. Without the time delay term, the model is described by an exponentially stable semigroup. We show that, under appropriate conditions involving the delay term, the…

The global existence and stability of the solution to the delay differential equation (*)$\dot{u} = A(t)u + G(t,u(t-\tau)) + f(t)$, $t\ge 0$, $u(t) = v(t)$, $-\tau \le t\le 0$, are studied. Here $A(t):\mathcal{H}\to \mathcal{H}$ is a…