Dynamical behavior of a third-order rational fuzzy difference equation

Abstract

According to a generalization of division (g-division) of fuzzy numbers, this paper is concerned with the boundedness, persistence and global behavior of a positive fuzzy solution of the third-order rational fuzzy difference equation $$x_{n+1}=A+\frac{x_{n}}{x_{n-1}x_{n-2}},\quad n=0,1,\ldots, $$ where A and initial values $x_{0}$ , $x_{-1}$ , $x_{-2}$ are positive fuzzy numbers. Moreover, some examples are given to demonstrate the effectiveness of the results obtained.