Impulsive Exponential Stabilization of Discrete Population Growth Models with Time Delays

The purpose of this paper is to investigate the impulsive exponential stabilization for the positive equilibrium points of a class of discrete population growth models with time delays. By using Lyapunov functionals, some new exponential stability criteria are given. It is shown that impulses can indeed make unstable equilibrium points exponentially stable, and when the impulses are employed to stabilize the unstable equilibrium points, the time interval between the nearest two impulses should be small enough, i.e., impulses should act frequently. Two examples are also presented to illustrate the effectiveness of the obtained results. It should be noted that, it's the first time that impulsive exponential stabilization results for discrete population models with time delays have been given.