Estimation Of Parameters And Asymptotic Distribution Of Food-Limit Species Model With Random Perturbation

The 21st century is a century of life science,the mathematical biology advanced rapidly, and the study in determinate system is perfect. In face,the species ecology systems are often subject to ,some uncertain factors,white noise,whether the presence of such noise affects these results that we have obtained has received exten sive attention ,which makes the study about stochastic system more and more important.In recent years ,with the rapid development of stochastic differential equation,it has permeated many fields, such as science, engineering ect.more over the estimating of the parameters of the stochastic differential equation by applying statistic methods will become an important discussion.Consider a random food limit species modelwhere B(t) is the 1-dimensional standard Brownian motion with B(0) = 0, t ≥ 0 with N(0) = N₀, and 0 < N₀ < K . By the Ito interpretation, Eq(1.2) is equivalent toThe existence of globally positive solutions ,global attraction of positive solutions ,the estimate and the consistence of parameters of Eq(1.3) are given by using both stochastic differential equation theories and numerical simulation.In this paper,we first prove when r >(1/2)a², the positive solution is global attrac-tive,And we carry numerical simulations for concrete model in S-plus, which strongly support our theoretical studies.At last,we obtain the maximum likelihood estimate and the consistence of the parameters of Eq( 1.3),through computing,we derive the asymptotic distribution of the parameters.