On The Dynamical Behaviors In Single-Species System With Contraception Control And Feedback Control

As we know, When a population is too high in nature, will bring a lot of troubleand loss. In order to solve this problem, we use contraception control technology. Con-traception control technology can directly and indirectly reduce the population, and willnot lead to sharp fuctuations in ecological system. At the same time, the real worldpopulations often can be afected by a variety of external factors, especially the adversefactors. Through the feedback control method can efectively eliminate the interferenceof the outside. Thus, the sterility control and feedback control in combination, can main-tain populations of sustainable development, and can inhibit the excessive number ofpopulation.In the paper, we will investigate the dynamical behaviors of nonautonomous single-species system with contraception control and feedback control from there factors. Theyinclude positive, boundedness, permanence, global stability.In the third section, in the nonlinear density restriction conditions, the positive,boundedness, permanence of nonautonomous single-species system with contraceptioncontrol and feedback is studied. And discussed respectively the boundedness, permanenceof nonautonomous single-species system with contraception control and feedback controlis studied.First, we get positive and boundedness of the solution of the system applicationof diferential inequality technique, Comparison principle and the construction of auxiliaryfunction method. Then we obtain the sufcient conditions for permanence of the systemthrough detailed analysis method.In the four section, in the linear density restriction conditions, the global stabilityof autonomous single-species system with contraception control and feedback control andthe global stability of autonomous single-species system with contraception control andfeedback control and infnite delay discussed by constructing lyapunov functionals.