Global behavior of two higher-order symmetric difference equations - Liu, Wanping,; Yang, Xiaofan, (Utilitas Mathematica, 2013)
Motivated by papers [3, 5] here we investigate the global asymptotic stability for positive solutions of the symmetric difference equation yn = (yn-kr-kyn-lr-lyn-mr + yn-kr + yn-lr + yn-mr)/(yn-kryn-lr + yn-kr - kyn-mr + yn-lr-lyn-mr+ 1), where 1 ≤ k < l < m and r ε (0,1], as well as of the somewhat simpler one yn = (yn-kr + yn-lr)/(1 + yn-kr - kyn-lr), where 1 ≤ k < l and r ε (0, 1]. Our main results extend the main results in [3, 5], where the cases when r = 1 were studied.