Allee Effect And Pulse Biodynamic System

Recently, the dynamic model with Allee effect has been widespread concerned, research-ing Allee effect on population survival and development, has becoming more important.themodel with impulsive control has play a important role in Population Dynamics. In thispaper, we analyze and formulate the Predator-prey model with Allee effect in the prey andthe dynamics of a three-trophic prey-dependent food chain system with impulsive controlFirst, The Allee effect in prey may be caused by predation or processes inherent tothe prey life history . We also discussed the different effects on prey with the strong Alleeeffect or the weak Allee effect. And we study boundness of solutions and the existence ofthe equilibria,obtain the suffcient conditions of locally asymptotically stable of the equi-libria, criterion, furthermore, analyze the global stability of the equilibria by constructingappropriate Lyapunov functions.Second, Species establishment in a model system in a homogeneous environment canbe dependent not only on the parameter setting,but also on the initial conditions of thesystem.In this paper,we deal with the prey-predator which the prey has the Allee effectsbecause of immigration or emigration, And we study boundness of solutions and the exis-tence of the equilibria,obtain the suffcient conditions of locally asymptotically stable of theequilibria.furthermore.Final, This paper considers the prey-predator model with a three-trophic food chainsystem with impulsive control,Nature enemies (predator) are released and pesticides areapplied impulsively to maintain the pest under the levels that cause economic damage. Weprove that, when the impulsive period is more than some threshold, the pest-eradicationsolution is globally asymptotically stable,and then we prove that,when the impulsive periodis lower than some threshold,the three-trophic prey-predator model is permanence.