The Analysis And Control Of Several Stochastic Population Models

For a long time, the study on biological population modelsis more important. Because most biological populations in nature areinfluenced by random disturbation in the process of development, it isnecessary to describe the population growth through stochastic processes.Reasonable estimations and controls of stochastic population models areof great theoretical and practical important significance to real data andtheory models and making full use of population resources. Based on theabove, three stochastic population models are proposed according to theprinciples of ecology and economics. The controllers are designed tomaintain the population persistence by using the statistical methods.The main contents of this paper are as follows:Firstly, based on random disturbation, the state variables are viewedas stochastic process and a stochastic model for a single population withlogistic growth is built up by thinking of state variables as stochasticprocesses. Using some methods in statistics, the model is linearized andthe corresponding differential equations of probability moment areobtained. According to the theory of large scale system, the stability fordifferential equations of probability moment is analyzed. Combining themeasure equation with state equations, the Calman filter is designed toget the optimal estimation of the state variables. On the basis of theoptimal estimation, according to the principle of economics, reasonableperformance is established, and the corresponding controller is designedto minimize the initial state to ideal state.Secondly, based on random disturbation, the state variables areviewed as stochastic process and a stochastic model for the populationwith age-structure is built up. In order to study the population influence,the corresponding differential equations of covariance function are givenusing some methods of statistics. Based on real data, the correspondingmeasure equation is given, and a Calman filter is designed to reduce theharmful disturbation of population growth and to maintain the balance ofecological system for population.Finally, based on random disturbation, the state variables are viewed as stochastic process and a stochastic prey-predator model is proposed.Using some methods in statistics, the model is linearized and thecorresponding differential equations of probability moment are obtained.The stability of the original model is analyzed by probability moment.In each section, the conclusions are verified by numericalsimulations.