一个广告脉冲模型的稳定性分析

Stability analysis of an advertising impulsive model

在离散时刻引入广告控制,给出使得广告策略的不稳定平衡点达到稳定的充分条件,得到了脉冲控制系统稳定的一个定理.通过改进的充分条件,达到脉冲间隔的一个上界,从而使得该脉冲控制的实现更为容易;并且得到了全局指数稳定和全局渐进稳定的结论.最后用Matlab软件对该模型进行数值仿真,验证了广告脉冲控制的有效性.

A sufficient condition is derived under which the unstable equilibrium point of the advertising strategy can be stabilized by advertising control at discrete moments, and a theorem on the stability of impulsive control system is derived. Through an improved sufficient condition, one upper bound of impulsive intervals can be obtained, thus the realization of this impulsive control is simpler; and the conclusion on global exponential stability and global asymptotical stability can be derived. The result is proved to be efficient through simulation with Matlab.