Impulsive stabilization of delay difference equations and its application in Nicholson's blowflies model

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.

Asymptotical stability of Runge–Kutta methods for nonlinear impulsive differential equations

“…Stability and asymptotic stability of implicit Euler method for stiff IDEs in Banach space has been studied by [22]. There is a lot of significant work on the numerical solution of impulsive differential equations, for example [6,7,10,14,[23][24][25][26][27]. However, in this work the authors did not investigate the stability of the numerical methods for non-stiff nonlinear IDEs under Lipschitz conditions.…”