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We study global behavior of the following max-type difference equation xn+1=max {1/xn,An/xn−1}, n=0,1,…, where {An}n=0∞ is a sequence of positive real numbers with 0≤inf An≤sup An<1. The special case when {An}n=0∞ is a periodic sequence with period k and An∈(0,1) for every n≥0 has been completely investigated by Y. Chen. Here we extend his results to the general case.

Global Behavior of the Max-Type Difference Equation xn+1=max {1/xn,An/xn−1}