Abstract
In this paper, a class of nonlinear difference equations with time-varying delays is considered. Based on a generalized discrete Halanay inequality, some sufficient conditions for the attracting set and the global asymptotic stability of the nonlinear difference equations with time-varying delays are obtained.
Highlights
Delay difference equations are an important class of discrete-time dynamical systems whose future states depend on the present states,and the past states
In the past few decades, delay difference equations have attracted considerable research interestbecause these equations play an essential role in discrete analogues and numerical solutions of delay differential equations.A massive literature on the stability analysis delay difference equations is available [1,2,3,4,5,6,7,8,9,10,11,12]
It should be noticed that the equilibrium point sometimes does not exist in many real physical systems, especially innonlinear delay difference equations
Summary
Delay difference equations are an important class of discrete-time dynamical systems whose future states depend on the present states,and the past states. It should be noticed that the equilibrium point sometimes does not exist in many real physical systems, especially innonlinear delay difference equations. It is more interesting for nonlinear delay difference equations to study the attracting set than to study the stability. Not much has been developed in the study of attracting setsfor the nonlinear difference equations with time-varying delays. Motivated by the above discussions, the main aim of this paper is to study the attracting setof the nonlinear difference equations with time-varying delays. Based on a generalized discrete Halanay inequality, some sufficient conditions for the attracting set and the global asymptotic stabilityof the nonlinear difference equations with time-varying delays are obtained.with no subheadings
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