Estimating Domains Of Attraction Of Nonlinear Systems Based On Moment Method

Estimating the domain of attraction of the system on the equilibrium point is a problem in the theory of stability analysis,which is widespread in the study of various fields.Such as estimating the domain of attraction of the predator-prey model,this result will help people more effectively control the various parts of the biological system,promote the balance of the ecosystem by studying various fields;estimating the domain of attraction of the tumor model,obtain the attraction domain of the equilibrium point will promote the tumor system to achieve tumor dormancy,which represents a clinical favorable condition.It is one of the quick and effective methods to estimating the attraction domain of the equilibrium point of the system by moment method.This method has been used in many epidemic models and the obtained results are ideal.The predator-prey model and the tumor model are also worthy of study in this method.In this paper,we study the problem of estimating the domain of attraction of nonlinear system,introduce two-dimensional predator-prey model and three-dimensional tumor model respectively,analyze the stability of the equilibrium point and estimate the domain of attraction by moment method,it consists of five chapters.In chapter 1,it introduces the concept of ecological balance,the form of predator-prey relationship,biology knowledge of tumor and research background of the domain of attraction of the system,as well as the results of the last few years.In chapter 2,some theorems of stability in the Lyapunov sense,the concept of the attraction domain,the method of moments and the domain of attraction problem was transferred into moment method are introduced.In chapter 3,we introduce a two-dimensional predator-prey model and transform the model,at the same time,the local stability condition of the predator-prey modal is given,estimating the domain of attraction by moment method,draw the corresponding image,more directly confirmation of the effectiveness of this method.In chapter 4,a three-dimensional tumor model is introduced,and the local stability condition of the tumor model is given,estimating the domain of attraction of the tumor model based on moment method,the proposed methodology can also provide an optimal strategy for cancer treatment.In chapter 5,the whole paper is summed up,proposes the advantages and disadvantages of the method and the problems which are still unsolved in the research.This article is composed of the above five chapters,estimating the domain of attraction of two nonlinear systems by the moment method,and obtaining the ideal result.