Dynamic behaviors of a class of high-order fuzzy difference equations (Q780462)

Summary: 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: \(x_{n+1} =\frac{Ax_{n-1} x_{n-2}}{B+\sum_{i=3}^k C_i x_{n-i}},\ n=0,1,2,\dots\), where \(x_n\) is the sequence of positive fuzzy numbers and the parameters \(A, B, C_3, C_4,\dots, C_k\) and initial conditions \(x_0, x_{- 1}, x_{- 2}, x_{-i}\) \((i = 3,4,\dots, k)\) are positive fuzzy numbers. Besides, some numerical examples describing the fuzzy difference equation are given to illustrate the theoretical results.