The Periodic Solution And Persistence For Two Classes Of Ecological Dynamical Systems

This thesis mainly deals with dynamics of two classes of ecological systems byusing coincidence degree theory, Lyapunov function method and comparison theo-rem of ordinary diferential equations, delay diferential equation basic theory andalmost periodic functional basic theory. These dynamics contain uniformly per-sistence, ultimate bound, global asymptotic stability, existence and uniquenessof positive periodic or almost periodic solutions. This paper is composed of threechapters.In the first chapter, the historical background and significance of the problemto be studied are introduced. Then, some excellent works in mathematical ecologyare summarized.In the second chapter, a class of delayed predator-prey system with stagestructure for prey and Holling Ⅲ functional response is discussed. By using thecontinuation theorem of coincidence degree theory and by constructing suitableLyapunov functionals, some sufcient conditions are obtained to guarantee theexistence, uniqueness and global stability of positive periodic solutions to the sys-tem. Then, numerical simulation is presented to illustrate the validity of our mainresults.In the third chapter, a non-autonomous dispersal prey-competition systemwith time delays and feedback controls is investigated. By using the theory ofcomparison theorem and delay diferential equation basic theory, a set of easilyverifiable sufcient conditions for the uniform persistence of the system are ob-tained. By means of suitable Lyapunov functionals and by using almost periodicfunctional basic theory, we prove that the prey-competition system is globallyasymptotically stable and the almost periodic solution of the system is unique un-der some appropriate conditions. We also give a numerical example to show theefectiveness of our results in this chapter.