Abstract
In this note we employ combinatorial arguments to count and classify certain periodic solutions of the delayed difference equationx(n) = f(x(n − k)), withk ≥ 2 given andn ∈ ℤ, The periodic solutions that we consider are formed by combiningk copies of anm- periodic solution of the “ordinary” difference equationx(n) =f(x(n- 1)). We also briefly discuss the possibility of braiding different periodic solutions of the ordinary difference equation into a periodic solution of the delayed version.
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Diekmann, O., van Gils, S.A. Difference equations with delay. Japan J. Indust. Appl. Math. 17, 73–84 (2000). https://doi.org/10.1007/BF03167337
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DOI: https://doi.org/10.1007/BF03167337