Abstract
In this article, we consider the impulsive stabilization of delay difference equations. By employing the Lyapunov function and Razumikhin technique, we establish the criteria of exponential stability for impulsive delay difference equations. As an application, by using the results we obtained, we deal with the exponential stability of discrete impulsive delay Nicholson's blowflies model. At last, an example is given to illustrate the efficiency of our results.
Highlights
Discrete systems exist in the word widely and most of them are described by the difference equations
In the practice, many systems are subject to short-term disturbances, these disturbances are often described by impulses in the modeling process, the impulsive systems arise in many scientific fields and there are many works were reported on impulsive systems [7,8,9,10,11,12,13,14,15,16]
The stability of impulsive delay difference equations has been studied in some articles, for example, see [18], there are few article concerning on impulsive stabilization of delay difference equations
Summary
Discrete systems exist in the word widely and most of them are described by the difference equations. The stability study for the impulsive system is one of the research focuses, see [11,12,13,14,15,16]. In the study of stability, the Lyapunov function and Razumikhin method were used by many authors, see, for example, [6,17]. The main aim of this article is to establish the criteria of impulsive stabilization for delay difference equations, using the Lyapunov function and Razumikhin method.
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