Determination of the Parameters of the Ecosystem

Based on the different kinds of the observation data about a predators-prey ecosystem,we studied the problem of determining the parameters.There are four different cases in the article.Case 1,when there is no error with the observation data and a parameter is known,then the other parameters can be accurately determined by its orbit and least squares method.Case 2,when there is still no error with the observation data,but no parameter is known,then in this case these parameters can not be accurately determined only by its orbit.However,through the effective grid research of the nonlinear model,at least four sets of data are needed to attain the high precisioon parameters.In case 3,there are errors with the observation data.We introduce a standard cycle,according to the cyclical nature of the solution to the ecosystem.Then we research on the determination of the parameters with the data of this standard cycle.Moreover,with the relation between the mean of predators and preys and the balance of the system,we adjust the parameters using grid research method.In case 4,when there are not only erros with observation data,but also with observation time,we modify the time first with relative optimal normal random numbers,then estimate the parameters with the same method used in case 3.