Abstract
We show that the embedding method described in J.-L. Gouzé and P. Hadeler (Monotone flows and order intervals, Nonlinear World 1 (1994), pp. 23–34) and H.L. Smith (The discrete dynamics of monotonically decomposable maps, J. Math. Biol. 53 (2006), pp. 747–758) leads immediately to the global stability results in M. Kulenović and O. Merino (A global attractivity result for maps with invariant boxes. Discrete Contin. Dyn. Syst. Series. B, 6 (2006), pp. 97–110). This allows the extension of some results on global stability for higher order difference equations due to Gerry Ladas and collaborators. Further, we provide a new result suggests that embedding into monotone systems may not be necessary for global stability results.
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