@article{Zhang2024, 
author = {Qianhong Zhang and Liqin Shen},
title = {Global asymptotic stability and trajectory structure rules of high-order nonlinear difference equation},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {10},
pages = {28256-28272},
keywords = {global asymptotic stability, trajectory structure, difference equation, nontrivial solution},
url = {https://www.sciopen.com/article/10.3934/math.20241370},
doi = {10.3934/math.20241370},
abstract = {In this article, global asymptotic stability and trajectory structure of the following high-order nonlinear difference equation   zn+1=zn−1zn−2zn−4+zn−1+zn−2+zn−4+bzn−1zn−2+zn−1zn−4+zn−2zn−4+1+b,n∈N,are studied, where  b∈[0,∞) and the initial conditions  zi∈(0,∞),i=0,−1,−2,−3,−4. Using the semi-cycle analysis method, in a prime period, a continuous length of positive and negative semi-cycles of any nontrivial solution appears periodically: 2, 3, 4, 6, 12. Moreover, two examples are given to illustrate the effectiveness of theoretic analysis.}
}