This article provides the formulas connecting Laguerre spectrum of output signal a linear discrete-time time-invariant delay system to its input signal. The Laguerre-domain representation is meaningful when square summable, and stable. A certain type polynomials arising in evaluation due presence time defined, key properties these are investigated. characterized by three-term recurrence relatio...

This paper deals with the dynamics of stochastic delay lattice systems fractional discrete Laplacian driven by nonlinear noise. The existence a invariant measure for nonlocal is established under certain conditions. idea uniform estimates on tails solutions, technique diadic division and Arzela-Ascoli theorem are employed to show tightness family probability distributions solutions.

This paper presents, explicitly, an approach to the exact calculation of group delay and its sensitivities with respectto component parameters basedon the adjoint network conceptand applicable to linear time-invariant circnits. In general, no more than four analyses are reqnired and the computational effort is only moderately more than is necessary for a single analysis. The resnlts presented a...

The marginal invariant density of chaotic attractors of scalar systems with time delayed feedback has an asymptotic form in the limit of large delay. It is well known that the dimension and the entropy of such attractors obey interesting scaling laws in this limit, but very little has been said about properties of the invariant density. We present general considerations, detailed analytical res...

This paper deals with set invariance for time delay systems. The first goal of the paper is to review the known necessary or sufficient conditions for the existence of invariant sets with respect to dynamical systems described by discrete-time delay difference equations (dDDEs). Secondly, we address the construction of invariant sets in the original state space (also called D-invariant sets) by...

We present an approach which allows to accurately predict both the occurrence and type of partially synchronous regimes of delay-coupled non-linear oscillators. Unlike the conventional approach, we build on an analysis of the stability properties of the synchronized equilibrium in the (coupling gain, delay) parameter space. As partially synchronous regimes are closely related to the presence of...

We study long run average behavior of generalized semi-Markov processes with both fixed-delay events as well as variable-delay events. We show that allowing two fixed-delay events and one variable-delay event may cause an unstable behavior of a GSMP. In particular, we show that a frequency of a given state may not be defined for almost all runs (or more generally, an invariant measure may not e...