Research Of An Approach On Global Asymptotic Stability Of Two ODE Models

In this paper,we consider two classes of ordinary differential equations(ODEs),which include some epidemic,predator-prey and chemostat models.By applying the comparison principle and differential inequalities to study the dynamic properties of ODEs,we obtain a threshold number R0 of the model and the stability properties of equilibrium.The result is applied to some models to recover or improve some results in the literature.The specific working process is as followsChapter 1,the purpose is to introduce the relevant research background and significance of ODEs model,focus on the biological background of epidemic,predator-prey and chemostat models,as well as the research status both domestic and foreign,and briefly explain the research contents and main work of this paperChapter 2,we mainly study the global stability of a class of ODEs for two species system including influx,which includes some epidemic and chemostat models.By applying a comparison principle and analyzing the vector fields,we get the global asymptotic stability of the trivial equilibrium of the model when R0?1 and obtain the global asymptotic stability of the unique non-trivial equilibrium of the model when R0>1.At the same time,numerical simulations are used to support the global asymptotic stability of the nontrivial equilibrium of the modelChapter 3,based on the discussion in Chapter 2,we mainly study the global stability of a class of ODEs including the logistic,which includes some predator-prey models.By applying a comparison principle and analyzing the vector fields,we get the asymptotic stability of the trivial equilibrium of the model when R0?1 and obtain the global asymptotic stability of the unique non-trivial equilibrium of the model when R0>1.Numerical simulations are used to support the asymptotic stability of the nontrivial equilibrium of the model.