Three Types Of Non-self-governing Prey - Predator Model With Periodic Solution

The periodical vibration in the ecosystem has great practical significance for people to protect the ecological balance and the biological diversity, so it is extremely important to study the periodical solutions.The periodical solutions of three kinds of systems were discussed in this paper.Its features are that a three-species clockwise chain predator-prey periodic system,with stage-structure and Beddington-DeAngelis functional response,was considered by using the Comparison principle and Lyapunov function, and the stage-structure was introduced to three-species periodic system. Then two-species systems in which predator has stage-structure,typeⅢfunctional re-sponse and cannibalism was studied. Besides,a type of three-species periodical sys-tem havingⅢfunctional response was discussed with reflective function developed by Mironenko.The content of this paper is as follows:1. The first chapter is the introduction.Firstly,the background and the research status of the system with stage-structure are introduced.Secondly, the research status of the three-species predator-prey system with Beddington-DeAngelis functional re-sponse is represented.Thirdly,the development of the theory of reflective function is introduced,and the problem which is considered in the second chapter is given.Finally, main works of this thesis are introduced.2.1n the second chapter,the basic concepts and the fundamental theories which are used in studying periodic systems are introduced, the Comparison principle and Lyapunov function are used in study the three-species system with stage-structure and Beddington-DeAngelis functional response at the same time.Sufficient conditions are obtained for the persistence,the uniform persistence,asymptotic stability, positive periodic solution and the existence.3.In the third chapter,the two species system was is cussed, in which the preda- tor has stage-structure andⅢfunctional response,the sufficient conditions that the system has positive invariant set and one positive periodical solution at least was ob-tained.4. In the fourth chapter, reflective function whose form likes R(t,x,y,z)= R(x,y,R3(t,x,y,z)) for the three-species periodic system with typeⅢfunctional re-sponse was given by reflective function theory.the necessary and sufficient conditions are content for special type of reflective function and the existence of periodic solution in the system has been established.