A Class Of The Population Competition System With Time Delay The Division Of The Stability Of The Region

This paper by the means relevant conclusion of ordinary differential equations stability theory and population competition model, establish the other model of two species competition system with time delay, and studies the global asymptotic stability of this model. The key work is to explore the effects of system stability the single delay existence in two species competition system, then give a stable region partition in the parameter plane and judge effectively for the stability region. The research question involves a number of practical background models, the conclusion which can be applied in the real nonlinear dynamic system model.In this paper, the main work includes the following sections:First of all, this paper briefly introduces the research background and the research significance. And, the research status of population dynamics and delay differential equations are introduced, which includes some new results of population dynamics in recent years and the new progresses of dynamical system theory stability.Secondly, this paper briefly introduces the involved basic theory of the research.They are:The first order ordinary differential equation stability conditions; The second order ordinary differential equation stability theory; Summarize equilibrium type and stability analysis table of the characteristic equation.Thirdly, This paper briefly introduces the involved basic species model. They are:The basic competitive species model; The generalized Logistic model of two species competition. Discuss the stability of the two species competition model, reasonably divide the stability region and give explanation population ecology.Finally, the main work of this paper is to study the stability of the two species competition system with time delay. First, simplify the generalized Logistic model of two species competition and introduce time delay parameter in order to establish two species competition model with time delay. Then, discuss the stability of the established new model, divide system stable region in the parameter plane using the theory of delay differential equations, combination the related conclusion of two species competition model in the second chapter; In the end, judge and draw a conclusion to the classified stable region.