Study On Dynamic Behavior For Several Kinds Of Fuzzy Difference Equations

With the development of science and technology,many specific mathematical models have been proposed in the fields of biology,economics,demography,automatic control theory and computer networks that require the application of difference equations to solve problems.It can be said that the difference equation is a powerful tool to describe the evolution for state variables with discrete time.Due to the uncertainty caused by the fuzziness to data,the combination of difference equation and fuzziness to data has aroused the enthusiasm and interest of many scholars.On the basis of summing up the predecessors,this paper mainly uses fuzzy number,lyapunov stability theory,inequality technique,mathematical induction,iterative method,transformation classification thought and other theoretical methods to discuss the dynamic behaviors with several types of fuzzy difference equations in detail,including the following contents:In the first part,the dynamic behavior of a five-order fuzzy difference equation is studied.The existence and uniqueness of the solutions,stability and convergence of the equilibrium point are studied by using α-cut set of fuzzy numbers,linearization theory,lyapunov equilibrium point theory and inequality technique.In the second part,the dynamic behavior of high order fuzzy difference equations is studied.The existence and uniqueness with the solution for the equation were analyzed by using the theory of fuzzy numbers and α-cut set,using jacobian matrix,linear equations and the theory of lyapunov stability studied the stability to the equilibrium point.Finally,the convergence to the equilibrium point with the system under certain initial conditions is proved by using mathematical induction,iteration and construction of sequence.In the third part,the dynamic behavior of the max-tpye fuzzy difference equation is studied.The existence and uniqueness of the solutions for the max-tpye fuzzy difference equation is similar to the existence and uniqueness to the solutions for the above two kinds of equations,then the periodicity of the solution with the equation was proved by classification and mathematical induction,and the specific periodic solution of the equation was obtained.Finally,the boundedness and sustainability of the solution are studied by the specific periodic solution of the equation.The software-package MATLAB 2016 was used for-numerical-simulation to theseequations,the obtained images vividly reflect the equation solutions change law and specifically verify the correctness of the conclusion.