We analyse numerically the bifurcation structure of a two-dimensional noninvertible map and show that different periodic cycles are arranged in it exactly in the same order as in the case of the logistic map. We also show that this map satisfies the general criteria for the existence of Sarkovskii ordering, which supports our numerical result. Incidently, this is the first report of the existence of Sarkovskii ordering in a two-dimensional map.
K. P. Harikrishnan and Dr. V . M. Nandakumaran, “Evidence for the existence of Sarkovskii ordering in a two-dimensional map”, Physics Letters A, vol. 133, pp. 305–308, 1988.