一类具有脉冲控制的传染性害虫模型

A Class of Mathematical Model Concerning Impulsive Pest Control Strategies

我们首先建立了具有脉冲控制的有关传染性害虫的数学模型,其模型是脉冲微分方程。进而,得到了控制变量的某个临界值。当有传染性的害虫的周期释放数目比这临界值大时,就会存在一个全局渐近稳定的边界周期解;当有传染性的害虫的释放数目比这临界值小时,该系统是持久的,这表示平凡的边界周期解失去了它的稳定性。

In this paper, we first propose a mathematical model concerning an impulsive pest control strategies. Therefore, our models are the impulsive differential equations. And then we obtain some critical value of control variable. It is observed that there exists a globally asymptotically stable boundary periodic solution when the amount of infective pests released periodically is larger than this critical value. When the amount of infective pests released is less than this critical value, the system is shown to be permanent, which implies that the trivial boundary periodic solution loses its stability.