Research Pest Control Model With Pulse Effect

In real life, pest problem is more and more attended, if not pest control timely,not only arouses serious economic losses, but also endangers human health.Considering the quickness of chemical control and non-polluting of biologicalcontrol, people often use integrated pest management methods to replace the lastchemical control measures for more theoretical and practical significance. Two kindsof pest control models with pulse effect have been studied and the dynamics behaviorof models has been analyzed in this paper. Main research contents are as follows：Considering the impact of natural enemies have constraints on the modelsdensity, the models of put predators and spray pesticides irregularly were constructed,using the theorem of Floquet, in the pest density is different, it is proved the pests arebounded; sufficient conditions which guarantee the existence of periodic solutionsand the locally asymptotical stability of pest-extinction periodic solution wereobtained. Using the theorem of impulsive differential equations, the globallyasymptotical stability of pest-extinction periodic solution were obtained, thepersistence of conditions were proved, using numerical simulation to verified thecorrectness of the conclusions, found change the ratio of insecticide to kill pests andthe predators density parameter of put in regularly are greater impact on the models.Considering the number of pests and natural enemies in different states, themodel which have two pulses were studied. Using the geometric function theory ofdifferential equations and successor function, the existence of order one periodicsolution is analyzed for the initial point falling with in different phase, given a classrail line to attract regional. At the same time the sufficient conditions for the track oforder one periodic solution is asymptotical stability by using the Poincare standardwere gained. The existence and attractiveness of order two periodic solutions wereproved by using the methods of analysis.