| The fuzzy difference equation is the difference equation whose coefficients or initial conditions are fuzzy numbers.It has uncertainty and can more accurately reflect the changing trend of the model system.Therefore,it has become one of important models by many scholars in their studies.This paper mainly uses generalized division.It is concerned with low-order exponential fuzzy difference equations,low-order nonlinear fuzzy difference equations with fuzzy number division and the global dynamic behavior of higher-order nonlinear fuzzy difference equations.We give some numerical examples to illustrate effectiveness of results obtained.The master s thesis consists of four chapters.In Chapter 1,it briefly describes the research status of the fuzzy difference equations,the research background and significance of the thesis,and the basic preparatory knowledge.In Chapter 2,firstly,we study the existence and uniqueness of solutions for exponential difference equation systemsWhere ai,bi,ci(i=1,2)and the initial values y0,z0 are positive real number.Secondly,the coefficient and the initial value are the fuzzy numbers,we discuss the existence of the positive solution and the stability of the equilibrium point for the exponential fuzzy difference equation xn+1=A+Bxne-Cxn.Where A,B,C and the initial value x0 are Positive fuzzy numbers.In Chapter 3,applying ?-sets,generalized divisions and other related theories,we study first-order nonlinear fuzzy difference equations Xn+1=M+xn+A/xn+B,n=0,1,2,....Where M,A,B and the initial value x0 are positive fuzzy numbers.It can conclude that the equation is globally asymptotically stable at the equilibrium point.IfIn Chapter 4,we study high-order nonlinear fuzzy difference equations xn+1=A+B/xn-m.Where A,B and initial value x-m,…,x-1,x0 are positive fuzzy numbers,the sufficient conditions for the existence,uniqueness,boundedness of the positive solution and the global asymptotic stability of the equilibrium point are obtained. |
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