Study On Property Of Solution Of Some Fuzzy Difference Equations

This Ph.D.thesis is divided into four chapters and main contents are as follows:In Chapter 1, we give a survey to the developments of fuzzy differential equa-tions and fuzzy difference equations. Then we introduce the background of prob-lems, the main results of this dissertation and some preliminaries are also sum-marized.In Chapter 2, we study respectively the first order linear fuzzy difference equation xn+1= Axn+B and the first order Riccati fuzzy difference equation xn+i =(?). By means ofα-cuts of fuzzy sets and some analysis techniques, the results about the existence, uniqueness, boundedness and persistence of the positive solution to these two models are obtained. A set of sufficient conditions are obtained for the stability of positive equilibrium point of these two models. Our conclusions are general and extend some existing ones.In Chapter 3, Three classes second order nonlinear fuzzy difference equations, that is are studied. By using ofα-cuts of fuzzy sets and the theory of the system of ordinary difference equations, the results about the existence, uniqueness, bound-edness and persistence of the positive solution to these models are obtained. Some sufficient conditions are established for the stability of positive equilibrium point and the oscillation of positive solution, respectively. Also, our results improve the known ones.In Chapter 4, we consider two kinds high order nonlinear fuzzy difference equations in the following By means ofα-cuts of fuzzy sets and the theory of the system of ordinary dif-ference equations, the results about the existence, uniqueness, boundedness and persistence of the positive solution to the two models are obtained. Some suf-ficient conditions are established for the stability of positive equilibrium point, respectively.