Analysis Of The Existence And Stability Of The Positive Equilibrium Solution Of A Mathematical Biology Model

The study about mathematical biology becomes more and more important in the21th century.The intersectant domain has been researched mainly between mathematical biology and othersubjects. Compared with the determinate mathematical biology model, species ecology system isoften confined environmental noise. It is widely concerned to research whether the presence ofenvironmental noise affected species ecology system and whether these results that we haveobtained varied for many researchers; Population dynamics is also one important branches ofbiomathematics, many authors are more interested in studying a stage-structured predator-preymodel.In this paper, we will first lead to mathematical biology model, then consider the existenceand uniqueness of the positive solution to a predator-prey model with modified Holling-type IIschemes with stochastic perturbation, and we mainly use two different methods to show that thereis a unique positive solution to the system with positive initial value. Based on this, we willcontinue to discuss the predator-prey with stage-structured prey. And we mainly use Lyapunovfunction, give out sufficient condition for it for global asymptotic and show it.