LAUSR

The purpose of this paper is to give the conditions for the existence and uniqueness of positive solutions and the asymptotic stability of equilibrium points for the following high-order fuzzy difference equation:xn+1=Axn−1xn−2/B+∑i=3kCixn−i n=0,1,2,…,wherexnis the sequence of positive fuzzy numbers and the parametersA,B,C3,C4,…,Ckand initial conditionsx0,x−1,x−2,x−ii=3,4,…,kare positive fuzzy numbers. Besides, some numerical examples describing the fuzzy difference equation are given to illustrate the theoretical results.