Dynamic Behavior Analysis Of Three Kinds Of Population Competition Models

In this thesis,by improving and extending a classical competition population,we establish a competition population model with nonlinear individual-averaged growth rate,two competition models with intra-and inter-specific competition terms,in which two species compete for the same resource.And a competition population model with nonlinear individual-averaged and seasonally varying growth rate,respectively.Through theoretical analysis and numerical simulations of the models,the long-term dynamic behavior of the models are studied,and the biological significance of the models are explained.In Chapter 1,the background knowledge and existing research on population competition are introduced,the study content of this these are presented,and some preliminaries are reviewed.In Chapter 2,a competition system of two populations with nonlinear individual-averaged growth rates is studied.Firstly,an invariant region of the system is obtained.Secondly,the existence and local stability of equilibrium points are discussed.Finally,the global stability of the interior equilibrium point(coexistence equilibrium point)is proved by using the theorem of Poincaré-Bendixson.The results of theoretical analysis reveal the conditions of exclusion or coexistence of two species.Chapters 3 and 4,models of two species competing for the same resource are established.In the third chapter,the dynamic behavior of the competition model of two species with intra-species competition terms is analyzed,and the existence and local stability conditions of the boundary equilibrium points and the interior equilibrium point are obtained.In addition,the global stability of the interior equilibrium point is also discussed,and numerical simulations are given to verify the results.Chapter 4 discusses the dynamic behavior of the competition model of two species with interspecific and interspecific competition terms.The existence and stability conditions of the boundary equilibrium point are obtained.The dynamic behavior of the interior equilibrium point is difficult to analyze.With the help of function monotonicity,concavity and convexity,the interior equilibrium point is analyzed by drawing the zero growth curves of the system to obtain possible existence of interior equilibrium points,and the corresponding phase diagram of each case is made to illustrate its stability.From numerical simulations,it is found that one or three internal equilibrium points may appear in the system.In Chapter 5,a competition model with seasonal succession and nonlinear individual-averaged growth rates of both populations was established.By analyzing the existence and stability conditions of the fixed point of the corresponding periodic map,the existence and stability conditions for the ordinary periodic solutions of the competitive system are obtained.In addition,sufficient conditions for the existence of nontrivial periodic solutions are obtained.Finally,the theoretical results are verified by numerical simulation and the effects of seasonal succession related parameters on the competition outcomes are discussed.In the last chapter,the main work of this paper is summarized briefly,and the main conclusions obtained in this paper are described,and some shortcomings in the article and future work are discussed.