Existence Of Multiple Periodic Solutions For Three Models With Harvesting In Mathematical Biology

Based on the existed three continue models, we obtain several classes of dis-crete delayed models with harvesting rate in mathematical biology which seemmore practical than those existed. In this paper, by employing a fixed point the-orem in regular cone and a continuation theorem in coincidence theory, we makemuch investigation for the existence of multiple periodic solutions of three mod-els in mathematical biology with harvesting rate. This thesis is composed of fourchapters.In Chapter 1, we introduce the backgrounds and significance of our studies,main work of this paper, preparing knowledge and some notions.In Chapter 2, we study a discrete for a generalized delayed population modelwith an exploited term. By applying a continuation theorem in coincidence theory,we obtain suffcient conditions which guarantee the existence of at least two directpositive periodic solutions.In Chapter 3, we study a Lotka-Volterra cooperative model with harvesting.By applying another continuation theorem in coincidence theory, we obtain suf-ficient conditions which guarantee the existence of at least four positive periodicsolutions of this system.In Chapter 4, we study a three-species predator-prey difference equation withnonmonotonic functional response and harvesting. By the same mean with Chapter3, we firstly obtain suffcient conditions which guarantee the existence of at leasteight positive periodic solutions of this system.For models with harvesting, from the works which have already done in theliterature, we can see that they often present complex dynamical behaviors. In thispaper we study three nonautonomous systems with harvesting rate and obtain someconcise suffcient conditions which guarantee the existence of two positive periodicsolutions, four positive periodic solutions, and eight positive periodic solutions indifference, the results we obtained reffect the complexity of these systems withharvesting to certain extent.