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On the fuzzy difference equation \(x_n = F(x_{n-1},x_{n-k})\). (English) Zbl 1452.39005

Summary: In this paper, we study the global asymptotic behavior of the positive solutions of the following fuzzy difference equation \[ x_n = F( x_{n-1}, x_{n-k}),\, n \in \{0, 1,\cdots \}, \] under appropriate assumptions, where \(k \in \{1, 2, \cdots\}\) and the initial values \(x_{-k}\), \(x_{-k+1}, \cdots, x_{-1}\) are positive fuzzy numbers. We give sufficient conditions under which every positive solution of the above equation converges to a positive equilibrium.

MSC:

39A99 Difference equations
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