Stability Of Solutions For Two Classes Of Stochastic Nonlinear Difference Equations

In this paper,the random SIR epidemic model and the exponential nonlinear difference equation are studied.Firstly,the stochastic continuous model is transformed into a stochastic discrete model by Euler-Maruyama method,and then linearized by Lyapunov function.Sufficient conditions for the progressive mean square stability of their solutions are obtained.This article mainly studies the following two aspects:On the one hand,a certain SIR epidemic continuity model expressed by differential equations was first introduced.Taking into account the interference of random factors,the Euler-Maruyama method was used to discretize the model,and a random discrete SIR epidemic model was obtained.Then the Lyapunov function method is used to linearize the model.Finally,the stability theorem of the stochastic difference equation is used to obtain the sufficient conditions for the asymptotic mean square stability of the equilibrium solution of the model.The rationality of the conclusion is verified by numerical simulation.On the other hand,this paper discusses how to apply the known results of stability theory to the stability of equilibrium points of a class of nonlinear difference equations with random perturbation,and considers a system of nonlinear difference equations with exponents.It is obtained that the system has a positive equilibrium solution and a sufficient condition for the stability of the positive equilibrium solution under the initial conditions is given.The image is obtained by matlab numerical simulation,and the correctness of the conclusion is verified.