Stability Of Solutions For Two Types Of Stochastic Discrete Models Of The Ecosystem

The deterministic and continuous model of biological population has been put forward and studied by many scholars,and many valuable and realistic theories have been obtained.But in the real world,most things are inevitably influenced by random factors,However,the original known model of biological population can not Slightlyreflect the reproduction and intrinsic nature of the population,so it is necessary to study the stochastic biological mathematical model.In this paper,the Euler-Maruyama method is used to transform the stochastic biological model into a random discrete model.By means of the knowledge of probability theory in discrete mathematics,the Kolmogorov's law of strong numbers and the random comparison theorem of discrete Ito? formula,the stability of solutions of two kinds of stochastic ecosystems is studied.The main contents of this paper are as follows: On the one hand,we study the asymptotic behavior of solutions for a class of linear stochastic difference equations.On the premise of some simple assumptions and discrete Ito? formula,the exact range of step h in the stochastic biological model is established.When h is small enough,sufficient conditions for the stochastic stability and instability of the solution of the equation are obtained.Finally,the correctness of the conclusion is verified by MATLAB numerical simulation.On the other hand,we study a class of 2-dimensional autonomous differential equations with stochastic disturbance,which combines the improved Leslie-Gower predation function with the Holling-type II model.Firstly,the random disturbance of biological system model caused by the deviation of the proportion of the population,the balance point deviation of the corresponding difference equation will be caused.Three equilibrium points of the stochastic equation can be changed and translated into the corresponding equilibrium points of the stochastic difference equation by the Jacobi linearization.Secondly,the sufficient conditions of stochastic stability and instability of the solution of the equation are discussed at each equilibrium point.Finally,MATLAB simulation is used to illustrate the correctness of the conclusion.