On The Nonautonomous Dynamical Predator-prey Species With Feedback Controls

So far, for the feedback controls model of species persistence, extinction, stability,existence of periodic solutions and so on has been a lot of research results. To examinethese dynamics model not only has a wide range of theoretical biology, but also hasimportant practical application value. This paper will discuss the two species predator-prey system with feedback control and predator-prey model with feedback control andinfinite delay of persistent and stability, as well as with a class of n-species predator-preymodel with feedback control of the extinction. The main contents are summarized asfollows:In the first section, we first introduce species with feedback control biology back-ground. Then introduce a variety of predator-prey and competitive model species withfeedback control . Finally, we will give in this article research content and organizationalstructure.Section II,This section is provision and give the lemma using in the following section.Section III, we introduce the persistence of two species Lotka-Volterra predator-preymodel with feedback control. Using a direct analysis method, direct the right side ofthe inequality system for zoom, these this types of models have been long-lasting newsu?cient condition. We further discussed the stability and of the extinction the speciesmodel.In section IV, Using a direct analysis method, direct the right side of the inequalitysystem for zoom, we study an infinite delay of non-autonomous species predator-preysystem with feedback control in the permanence.In section V, This section is summarize and discussion.