In this paper, we study the dynamical behaviors of neutral differential equations with small delays. We first establish existence and smoothness global inertial manifolds for these equations. Then further prove respect to delays a certain class The method can be also applied deal more general small-delay systems. Finally, apply our main results van der Pol oscillator model delay.

We give an explicit formula for the general solution of a one dimensional linear delay differential equation with multiple delays, which are integer multiples of the smallest delay. For an equation of this class with two delays, we derive two equations with single delays, whose stability is sufficient for the stability of the equation with two delays. This presents a new approach to the study o...

In this paper, a general setting is presented to study the exponential stability of discrete-time systems with bounded or unbounded delays. Based on M-matrix theory, we establish sufficient conditions ensure global zero equilibrium low-order, and high-order, Hopfield neural network models delays delay in leakage terms. A comparison literature shows that our results generalize improve some recen...

This paper proposes an input/output interpretation of supervision of discrete event systems. New concepts must be introduced in order to describe the behavior of the closed-loop system of plant and supervisor subject to communication delays. This paper further characterizes the class of supervisors allowed under delays for the general case and for additional assumptions on the plant language.

The work is devoted to the problems of estimating time delays that arise in studies using method three-dimensional electrical impedance tomography. block diagram hardware-software complex tomography considered. A general algorithm for visualizing internal structures object under study by described, and it shown which parts affect occurrence delays. Methods minimizing occur during research are w...

We study general stochastic birth and death processes including delay. We develop several approaches for the analytical treatment of these non-Markovian systems, valid, not only for constant delays, but also for stochastic delays with arbitrary probability distributions. The interplay between stochasticity and delay and, in particular, the effects of delay in the fluctuations and time correlati...

Due to the plentiful dynamical behaviors, integro-differential equations with delays have many applications in a variety of fields such as control theory, biology, ecology, medicine, etc [1, 2]. Especially, the effects of delays on the stability of integro-differential equations have been extensively studied in the previous literature (see [3]-[9] and references cited therein). Besides delays, ...

A general class of linear time-invariant feedback control systems with a distributed delay in the feedback line is treated. Differently from present literature, both limits of the delay are taken as non-zero, which brings an interesting new perspective to the problem. The authors start with a theorem stating the equivalence of a general class of such distributed-delay systems to a system with m...