Several Types Of The Differential System Perturbation Method Research

Perturbed diferential systems widely exist in practical problems, there is a strong prac-tical background and generate a lot of applications, has aroused the concern of many scholars.In addition, the speed of the power system is also widely present in the practical problems itis characterized by the system is divided into two types of fast state and slow state systemPerformance characteristics by the slow state, expressed in the equation is the highest levelof the equation by far less than a positive small parameter, belongs to the boundary layersingular Perturbation of such systems is also widespread in biomathematics of infectiousdisease dynamics, but by using perturbation methods to study speed type power Systemand the infectious disease model or rare on perturbation theory and its speed system Intheoretical research and application of very important signifcance.Perturbation theory from the perspective of dynamical systems, based on a variety ofperturbation methods. So far, many scholars at home and abroad Perturbed system andpower system speed to do a lot of research of this thesis is to be improved for general singu-larly perturbed systems and the speed of dynamical systems model to study the Solution,and with the infectious disease model and related research.In this thesis, the following question:(1) for a class of singular perturbation of linear boundary value problem, according to themost high-end and high-end order diferential reduced-order Then use the method of multiplescales, depending on the boundary layer to introduce the stretched variable structure Theasymptotic solution of the boundary value problem, and this asymptotic solution to analyze,draw the appropriate conclusions.(2) will be the speed-power system is extended to non-local problem for a class ofnonlinear speed system. First, in the appropriate manner under the conditions of use ofthe method of multiple scales in the perturbation theory, Introduce the stretched variabledepending on the boundary layer and the power series expansion theory, the problem inthe form of asymptotic solution, we prove the existence Re-use the theory of diferential inequalities to prove the uniform validity of the formal asymptotic solution in the entireinterval.(3) (2) based on the theory, try a combination of perturbation theory and biomathe-matics SEIR epidemic model. First use of bio-mathematical form of this model the kineticanalysis, Then use the regular perturbation method in the perturbation model constructedthe formal asymptotic solution, and then use the theory of diferential inequalities to provethe existence and efectiveness of this solution. Finally, the advantage of the model resultsobtained by the two methods of numerical simulation, and simulation results are analyzedand compared to verify the feasibility of the perturbation method in the model.In this paper, the perturbation method, diferential inequality, power series theory andboundary layer theory to study the three types of perturbation solution to the model in whichthe second based on the existing Of the low-order odd perturbation model of the HigherOrder Singular Perturbation Boundary Value Problems, Chapter III to consider the speed ofthe system on the basis of non-local problem, Chapter Infectious Disease Model Combinedwith the perturbation on the model is analyzed on the basis of the kinetic analysis, usingthe perturbation method, proved the feasibility and rationality of the solution, Provides atheoretical basis for the analysis of a class of infectious disease model in the future.