Research On The Parameter Estimation Of The Two Species Predator-prey Model And Its Properties Via Numerical Differentiation

Recently, the study of mathematical model produced a wide range of development, in which the analysis of complex system is involved many areas. Such as biology, environment, economic, material processing engineering and so on. A general research method is contributing a mathematical model to a randomness complex system. And in the basis of computer simulation we find the evolution of this dynamic system. Then we can forecast, organize and control the system.Currently, using observational data of the inverse problem of differential equations, that is the parameter estimation of differential equations, is a hot issue of probability and statistics in the international research filed. Many scholars use predator-prey as the simulation object in the study of the parameter of differential equations. Therefore, it is necessary to research in-depth and detailed on parameter estimation of the two species predator-prey.In this paper, we introduce a new estimation method two-stage estimation to study the estimation of parameters in the 2-species predator-prey model. In the first stage, we use observations to solution differential estimation based on finite difference theory. In the second stage, we transform the parameter estimation of predator-prey model into a linear least squares problem. This method greatly reduced the computation and improved the speed. Then we have study to two stage method in detail, give a statistic model of parameter estimation of differential estimation in a general sense, and discuss the large sample properties of two stage method. Finally, we have the numerical simulation to 2-species predator-prey model of parameter estimation. The result shows that the proposed method is effective.This paper is composed of five parts. In the first chapter, we introduce the historical background of the problem and prerequisites required in this paper. In the second chapter, we give the statistic model in theory first, and discuses the parameter estimation problem in detail, then give a based on finite difference numerical differentiation of two stage parameter estimation. And in the third chapter, we discuss the consistence and asymptotic normality and other large sample properties of two stage parameter estimation. In the forth chapter, we are simulated to the parameter estimation of two species predator-prey model. And analysis parameter estimation of three general finite difference numerical differential. Then we compare then result to nonlinear least square estimation and other reference results. It shows that the result in this paper is feasible. In the fifth chapter, we have a summary for this paper, and give the research forecast.