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He, Qiuli; Tao, Chunyan; Sun, Taixiang; Liu, Xinhe; Su, Dongwei

Periodicity of the positive solutions of a fuzzy max-difference equation. (English) Zbl 1474.39029

Abstr. Appl. Anal. 2014, Article ID 760247, 4 p. (2014).
Summary: We investigate the periodic nature of the positive solutions of the fuzzy max-difference equation \(x_{n + 1} = \text{max} \left\{A_n / x_{n - m}, x_{n - k}\right\}, n = 0,1, \ldots\), where \(k, m \in \{1,2, \ldots \}\), \(A_n\) is a periodic sequence of fuzzy numbers, and \(x_{- d}, x_{- d + 1}, \ldots, x_0\) are positive fuzzy numbers with \(d = \left\{m, k\right\}\). We show that every positive solution of this equation is eventually periodic with period \(k + 1\).

Cited in 5 Documents

MSC:

39A23 Periodic solutions of difference equations
34A07 Fuzzy ordinary differential equations
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