Research On The Asymptotic Behavior Of The Equilibrium Points And Positive Solutions Of Several Types Of Nonlinear Fuzzy Difference Equations

The real world mainly contains two kinds of uncertainty phenomena,namely random uncertainty and fuzzy uncertainty.Probability theory is a powerful theoretical tool to deal with random uncertainty phenomena,and fuzzy mathematics is a mathematical theory to deal with fuzzy uncertainty phenomena.The fuzzy difference equation is a mathematical model that characterizes the discreteness of the fuzzy uncertainty in the model.The model parameters and initial conditions in the system are fuzzy numbers,and the solution of the system is the fuzzy number sequence.This thesis mainly studies the dynamic behavior of the positive solutions of three types of fuzzy difference equations,include the second-order exponential fuzzy difference equation model xn+1=Axn+Bxne-xn-1,n=0,1,2...,the second-order nonlinear rational fuzzy difference equation model xn+1=xn/xn+xn-1+A,n=0,1,2....and the second-order rational exponential fuzzy difference equation xn+1=A+Be-xn/C+xn-1,n=0,1,....The ? cut set models the one-dimensional fuzzy difference equation into a two-dimensional parameter difference equation system.Using the comparison principle and mathematical induction of the difference equation,the bounded and persistent dynamic behavior of the positive solution of the constant difference equation is obtained.The linearization method,the eigenvalues of the matrix,and other methods are used to obtain sufficient conditions for the local stability and global stability of the positive equilibrium solution of the model.Second,the dynamic behavior of the solution of the corresponding fuzzy difference equation model is studied by the generalized division of the fuzzy number(g-division).Under certain conditions of the model parameters and initial conditions,the boundedness,persistence,existence and convergence of positive fuzzy solutions of the corresponding fuzzy difference equations are obtained.Finally,the validity of the theoretical conclusions is verified by numerical examples This method has been initially applied to the study of the dynamics of biological populations and the fluctuation of stock prices in financial markets,and has obtained relatively good results.