Parameter Estimation for Predator-Prey Equations Using Hidden Periodic Model

In this paper, we propose a new two-stage estimation (TSE) method for estimating parameters in two species predator-prey model. In the first stage, we use the hidden periodical model in time series analysis to fit the state variable and their derivates, since the solutions to the predator-prey model have periodical properties. To consider the properties of the solutions to the ordinary differential equation (ODE) is ignored by all of the research in parameter estimation for ODE so far. And then the parameter estimation for ODE is transformed into a linear regression model. So the second stage is just an ordinary regression analysis. Our new TSE don´t need numerical solve the ODE and is easy to be carried out. Especially, we can obtain the interval estimation of the parameters that is also ignored in most research up to now. The simulation study show that the relative errors of the point estimates is great smaller than the published results (eg, see[2, 3]) and our method is suitable from the view point of statistics.