Dynamic Behavior Of Three Kinds Of Predator Systems

In recent decades,the rapid development of mathematical ecology,predator prey system as one of the basic relationship between the two groups.Studying its dynamic behavior has become a common concern for biologists and mathematicians.Today,a lot of research work for the dynamic behavior of predator-prey system has been carried out,and achieved some results.However,some of these studies did not take into account the impact of the impulsive,feedback control,harvesting term and other ecological factors.Therefore,in this thesis,we will research the following three parts:Firstly,permanence and asymptotic behavior of a non-autonomous Holling?predator-prey for two species is proposed and studied.With the non-autonomous single pulse system has researched for continued survival and extinction.First using the comparison theorem of differential equations and inequalities appropriate scaling to obtain permanence to the system systems;secondly using the comparison theorem of differential equations and constructing suitable Lyapunov function to obtain system prey extinction predator prey extinction and global asymptotic stability condition.Respectively,our results show that to ensure the system permanence extinction and global asymptotically stability impulse played an important role.Secondly,a two species Lotka-Volterra predator-prey system with impulse is proposed and studied.By using Mawhin's continuation theorem of coincidence degree theory and some analysis approaches,sufficient conditions which guarantee four positive almost periodic solutions are obtained.Since the condition has nothing to do with the delay.Therefore,when delay is zero,the system becomes model Zhao and Ye in the[19].when the coefficients of the system is periodic function,then corollary 4.1 to get[19]conclusion,so our results improve the main results of[19].Finally,a Hassell-Varley-Holling ? response function predator-prey discrete system with feedback control is proposed and studied.First,sufficient conditions for the permanence of the system are established by applying the comparison theorem of difference equations and some suitable variable change.Compared with the[43],We found the feedback control system variables have a little impact on persistent bounds of predator prey,but the entire system under certain conditions can persistence.Then,assuming that the coefficients of the system is almost periodic sequences,we obtain sufficient conditions for the existence and unique of the almost periodic solution by Cheban and Mammmana proposed the theory of almost periodic solution of difference equation.Moreover,the almost periodic solution is uniformly asymptotically stable.In addition,this section also got a corollary,when the coefficients of the system is periodic sequences,periodic system solution also exists which is uniformly asymptotically stable.An example together with numerical simulation indicates the feasibility of the main result.