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On the system of rational difference equations xn+1 = f(xn,yn-k), yn+1 = f(yn, xn-k)

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Abstract:

We study the global asymptotic behavior of the positive solutions of the system of rational difference equations xn+1 = f(xn,yn-k), yn+1 = f(yn, xn-k), n = 0,1,2,..., under appropriate assumptions, where k ∈ {1,2,...} and the initial values x-k, x-k+1,...,x0, y-k, y-k+1, ..., y0 ∈ (0,+∞). We give sufficient conditions under which every positive solution of this equation converges to a positive equilibrium. The main theorem in [1] is included in our result.

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