Qualitative Analysis Of Some Fuzzy Difference Equations

The difference equation,as a powerful tool to describe the real life law,has been widely used in various fields.During the past half century,scholars have found that the known information needed to describe the difference equation model in many practical problems is fuzzy.Therefore,the theory of fuzzy difference equation is established by combining the theory of fuzzy mathematics with the classical difference equation theory.In this paper,the relevant properties of the solutions of the higher order fuzzy difference equations and the max-type fuzzy difference equations are investigated.The full text will be based on the fuzzy set to study the difference equation,the basic structure is as follows:In the first chapter.First,the background,significance and current situation of fuzzy difference equations are briefly introduced.Secondly,the basic concepts and basic conclusions that need to be used in this article are explained.Finally,the main research works in this paper are outlined.In the second chapter,the qualitative analysis of a class of five order fuzzy difference equations is carried out.By using the concepts and properties of fuzzy sets,?-cuts,reduction to absurdity,the existence and uniqueness of the solution are demonstrated.In addition,by using the linearization theory and the mathematical induction,the local asymptotic stability,the global asymptotic stability and the instability at the four equilibrium points of the fuzzy difference equation are discussed.Finally,the correctness of the theoretical analysis is verified by using the software of MATLAB.In the third chapter,the existence of solutions of a class of high order nonlinear fuzzy difference equations is studied.The sufficient conditions for the local asymptotic stability,instability and global attractivity of the equation at the zero equilibrium point are discussed respectively,and the sufficient conditions for the existence and instability of the non-zero equilibrium point are discussed.In addition,the boundedness of the solution of the equation is proved by the mathematical induction,and the sufficient conditions to guarantee the boundedness of the solution are obtained.Finally,the simulation of the equation is carried out to verify the correctness of the conclusion.In the fourth chapter,the dynamic properties of a class of max-type fuzzy difference equations are investigated.By using ?-cuts of fuzzy sets,inequality technique,analytic hierarchy process,the iterative method,the periodicity and boundedness of the solution of the equation have been proved,and the analytic form of periodic solution is obtained.Finally,the periodicity of the solution is verified by the software of MATLAB.In the fifth chapter,the research work carried out in this paper is summarized,and the future research work is put forward.