We consider two types of nonautonomous two-periodic Gumovski–Mira difference equations. We show that while the corresponding autonomous recurrences are conjugated, the behavior of the sequences generated by the two-periodic ones differ dramatically: in one case the behavior of the sequences is simple (integrable) and in the other case it is much more complicated (chaotic). We also present a global study of the integrable case that includes which periods appear for the recurrence.
Cima, A.; Gasull, A.; Mañosa, V. Non-autonomous two periodic Gumovski-Mira difference equations. "International journal of bifurcation and chaos", Desembre 2012, vol. 22, núm. 11, p. 1250264-1-1250264-14.