This paper is concerned with local stability, oscillatory character of positive solutions to the system of the two nonlinear difference equations x_(n+1) = A + x_(n-1)~p/y_n~p and y_(n+1) = A + y_(n-1)~p/x_n~p, n = 0,1,..., where A ∈ (0, ∞), p ∈[1,∞), x_i ∈ (0, ∞), and y_i ∈ (0,∞), i = -1,0.
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