| The theories and methods of impulsive differential equations have got great development and become a integrated system in recent years.It is widely applied in various fields such as population dynamics,epidemiology,medicine dynamics,bio-cybernetics,genetics and chemical reactions.Pest control plays an irreplaceable role in agricultural production.In order to simulate the dynamical behavior of pest populations,it is essential to construct mathematical models,especially to describe the pest population dynamics by using impulsive differential equations.It is more reasonable and precise to describe the pest population dynamics by impulsive differential equations,which reflects all kinds of change orderliness,since the reproduction and damage of pest,human control behavior are almost periodic in the natural world.Based on the Integrated Pest Management(IPM)strategy,in this paper,we establish a class of ecological models concerning impulsive effects(that is,release natural enemies at fixed times),and investigate the dynamical behavior of these ecological models,by using Floquet theory and methods of impulsive differential equations.We prove that all solutions of the system are uniformly eventually bounded.Using Floquet theorem and impulsive comparison theorem,it is proved that the pest eradication solution of the system is globally asymptotically stable if the impulsive period is less than a certain critical value,by using Floquet theory and impulsive comparison theorem.Otherwise,the system will be permanent(that is,survive continuously).Finally,in order to verify our theoretical results,the dynamical behavior of the proposed model is discussed by means of computer numerical simulation,including the existence,persistence,comprehensiveness and stability of the periodic solution of the system.Based on the results obtained in this paper,a theoretical method is given by using integrated pest management strategies in agriculture to control pest,from a mathematical point of view. |
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