| In the 21st Century, the study about mathematical biology becomes more and more important. However, in real life, population ecology systems are inter-fered by environmental noise. Therefore, to study whether environmental noise influences population ccology system and whether the existing results change has attracted considerable attention. It has application value and practical signifi-cance for this thesis to use stochastic analysis, random dynamical system theory and statistical methods as tools to study the asymptotic behavior of random reef model and parameter estimation problem. Specific research contents are as followsThe first chapter describes the background and significance of the research,as well as some preliminary knowledge, and introduces the main content and framework of this thesis.The second chapter mainly studies the persistence and extinction of random coral reef model. By using the Markoff theory, invariant measure, ergodic theory,the law of large numbers and martingale inequalities and other related theories,it researches the Porder solutions of stochastic coral reef model boundedness, the existence of positive solutions of recurrent and stationary distribution, solution for further study of the persistent random model of coral reefs and extinction.The third chapter mainly studies the stochastic model of nonlinear noise driven coral reefs in the boundary of the asymptotic behavior with stochastic processes, boundary theory, invariant measure, ergodic theory and martingale inequality theory. Firstly, it focus on the existence of the solutions of random coral reef model corresponding to the Fokker-Planck equation so as to study the random coral reef model boundary asymptotic behavior. Secondly, it turns to the estimation of random reef model solution to study the coexistence problem of random coral reef model.The fourth chapter mainly studies the parameter estimation and numerical simulation of random reef model. Above all, the model is discretized by Euler discretization method , and then studied by using the theory of maximum likeli-hood estimation method. Afterwards, there come the estimation results of each parameter by numerical simulation, which shows the square error of maximum likelihood parameter estimation the dependence on the sample size. However,under the hypothesis of normal distribution, the maximum likelihood estimate and the true value have no obvious difference, therefore, the maximum likelihood estimates of the parameters is very good. |
