Study On The Estimation Of Parameters Of The 2-Species Predator-Prey Model

The research of mathematical biology model has got the extensive application through the development of a century. At the same time, estimation of the Ordinary Differential Equations (ODE) has appeared. Presently, many methods for estimating parameters from noisy data are computationally intensive and often fit poorly with the real data. Consequently, study for a method with high precision becomes more and more important.Lately, Ramsay etc. have given an estimation method of parameters in the 2-species predator-prey model by treating the spine functions as the basis system. However, they didn't make most use of qualitative property of the model such as the periodicity. In this paper, we introduce a new the estimation method two-stage estimation (TSE) to study the estimation of parameters in the 2-species predator-prey model. First, x(t) is showed as the Hidden Periodic Model (HPM) by treating the trigonometric function as the basis system. Using the estimation method of the Hidden Periodic Model (HPM), we estimate K_i by observing the diagram of |S_N(λ)| and estimate the angle frequencyω_ik and the original phaseφ_ik. Next, the problem is transformed the least square problem and other problems are estimated. Finally, combined with real data, numeric simulation has been done and shows that the method is truly feasible.This paper is composed of five parts. In the first chapter, we introduce the historical background of the problems which will be investigated, the main results and some definitions and lemmas which are required in this paper. In the second chapter, we discuss Numerical Differentiation and its Property of stochastic datum. And in the third chapter, we discuss the estimation method of each parameter in the 2-species predator-prey model in detail. At in the forth chapter, we produce a group of observation data by using the real value of the parameter. According to the observation data we use the method introduced in this paper to estimate the parameters, which shows the results are better than those given in pertinent references. So the method in this paper is feasible. At last, we conclude the paper and give the research forecast.