On the fuzzy difference equation xn = F(xn-1, xn-k)

Abstract In this paper, we study the global asymptotic behavior of the positive solutions of the following fuzzy difference equation x n = F ( x n − 1 , x n − k ) , n ∈ { 0 , 1 , ⋯ } , under appropriate assumptions, where k ∈ { 1 , 2 , ⋯ } and the initial values x − k , x − k + 1 , ⋯ , x − 1 are positive fuzzy numbers. We give sufficient conditions under which every positive solution of the above equation converges to a positive equilibrium.

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