Abstract

In these three papers, the authors study the differences equation xn+1=(xαnxβn−1xγn−3+xαn+xβn−1+xγn−3+a)/(xαnxβn−1+xβn−1xγn−3+xαnxγn−3+1+a) with nonnegative entries, where α=1, β=γ in the first [ibid. 6, No. 41–44, 2109–2116 (2011; Zbl 1256.39010)], α=γ, β=1 in the second [ibid. 6, No. 41–44, 2117–2124 (2011; Zbl 1256.39011)], and α=β, γ=1 in the present third paper. In particular, they study the structure of the semicycles of oscillating solutions around the equilibrium 1, and the authors show that the last one is globally asymptotically stable.