[PDF] Top 20 Stability of a delay difference system

... where B is an (m × m) real matrix, x n : N → R m , a positive integer k is a delay, was inves- tigated by Levitskaya [10]. She transferred Rekhlitskii’s result [16] about the di ff erential equation ˙ x = Ax(t − ... See full document

... | tr B | < 1 + det B < 2 (2.5) because det A = det B − tr B + 1 and tr A = tr B − 2. This coincides with the Schur-Cohn necessary and sufficient condition for the asymptotic stability of the zero solution of ... See full document

... then there exists a unique uniformly asymptotically stable almost periodic solution q(n) of system (.) which satisfies |q(n) | ≤ B ∗ for all n ∈ K . In particular, if g(n, φ) is periodic with period ω, then ... See full document

... In the stability literature, we can find two major trends: stability using the first approximation Lyapunov method and the direct Lyapunov functional method. For this latter trend, see Zhang and Chen [12], ... See full document

... predator-prey system with time delay due to the gestation of the predator and stage structure for both the predator and the prey is ...local stability of the predator-extinction equilibrium and the ... See full document

... Time delay is one of sources of instability and poor performance, so that dynamic systems with time delay have received extensive attention and research. Meanwhile, fractional- order systems have gained ... See full document

... of Difference Equations has been growing ...that difference equations appear as mathematical models describing real life situations in probability theory, queuing theory, statistical problems, stochastic ... See full document

... the delay-dependent stability criteria, in which some useful approach can be effectively used to analyze the stabilization for linear neutral sys- tems with ... See full document

... the stability of the systems as well as the regularity and also impulse free (in case of continuous singular sys- tems) or causality (in case of discrete singular systems) [2, 11, ...time system is often ... See full document

... the stability of the equilibrium of neural networks. Thus, the stability analysis is a necessary step for the design and applications of neural ...Therefore, stability analysis of neural networks has ... See full document

... the stability analysis under arbitrary switching problem (i) which will be focused on in this work deals with the case that all subsystems are ...whole system un- stable. In addition, stability under ... See full document

... predator-prey system is the basic model in pop- ulation dynamics, so the interactions between predator and prey in natural ecosystem have drawn extensive attention from scholars in different kinds of ...and ... See full document

... of delay systems have been a major research subject in differential equations (see, ...time delay on the feedback term (internal or at the boundary) in a wave equation can destabilize the system, ... See full document

... Gnedenko system with multiple delay vacations of a ...this system as well as its stability is important in terms of theory and ...asymptotic stability of the dynamic solution and showed ... See full document

... The paper is organized as follows. In Section , we introduce some notations, definitions, and a proposition. In Section , we give new criteria for exponentially practical stabil- ity of impulsive discrete time systems ... See full document

... In this section, we give a theorem on the structure of the matrix Sn, and provide an example for illustration. The results in this section are discrete analogues of the ones given in 1 . Theorem 2.1. The homogeneous ... See full document

... (LPD) delay system and LPD control delay ...exponential stability with a given convergence rate and asymptotically stability of lin- ear parameter dependent (LPD) delay ... See full document

... time delay, µ 1 , µ 2 , f µ 1 , f µ 2 , µ f f 1 , f f µ 2 are pos- itive real ...This system is subjected to the Dirichlet boundary conditions and to the initial conditions which belong to a suitable ... See full document

... In this paper, we provide a differential model to describe the dynamic behavior of the Hasting-Powell food chain system. And two different Schrödingerean delays are incorpo- rated into the model. The stabilities of ... See full document

... Result Analysis: From, above part we completed the proofs of only if part for strong stability of nonlinear difference system. This plays the important role in signal proceing units and ... See full document