Study Predator-prey Models With Impulsive Control To Pest

Since impulsive population dynamic systems have enormous potential in wide vari-eties of applications, many specialists and scholars apply themselves to the research of thetheory and achieve many perfect productions. Especially in control strategy for pest, withthe development of impulsive differential theory [7,8], impulsive differential also describesthe evolving process and the control process of species which make the mathematicalmodels of the control process more reasonable. A lot of experiment illustrates that im-pulsive control to pests has very important theoretical and practical meaning to reducethe plague of the past and improve the level of economy.In this paper, we mainly investigate three kind of Impulsive control of the Lotka-Volterra predator-prey systems for pest from three facts and analyze the initial andboundary problems. Based on the comparison theorem and upper and lower solutions,some conditions which the models have solutions are obtained.1. Firstly, in the three section, we introduce a Lotka-Volterra predator-prey systemwith impulsive control and no density restrain to prey, we obtain the conditions whichthe model has solution. The corresponding results given in [1] are improved, the resultsare more brilliant.2. In the four section, a Lotka-Volterra predator-prey system with impulsive controland density restrain to prey is investigated, we discuss the time-limited pest control of aLotka–Volterra model with impulsive harvest by mathematical methods on finite timeand control the density of the pest to a lower level.3. In the five section, we study a Lotka-Volterra predator-prey system with impulsivecontrol and the functional response to predator. The existence of solutions are obtainedby using the Comparison principle for impulsive di?erential equations and inequalitytechniques. And some examples to illustrate the conclusions obtained in this paper aregiven as the application of theorems.