@article{Alotaibi2022, 
author = {A. M. Alotaibi and M. A. El-Moneam},
title = {On the dynamics of the nonlinear rational difference equation              x              n        +        1              =                    α                              x                          n              −              m                                                      +                  δ                                    x                          n                                                  β      +      γ                        x                      n            −            k                                                            x                      n            −            l                                                  (                                                            x                                  n                  −                  k                                                                              +                                                                  x                                  n                  −                  l                                                                                        )},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {5},
pages = {7374-7384},
keywords = {difference equations, rational difference equations, qualitative properties of solutions of difference equations, equilibrium, oscillates, prime period two solution, globally asymptotically stable, points},
url = {https://www.sciopen.com/article/10.3934/math.2022411},
doi = {10.3934/math.2022411},
abstract = {In this paper, we discuss some qualitative properties of the positive solutions to the following rational nonlinear difference equation              x              n        +        1              =                    α                              x                          n              −              m                                                      +                  δ                                    x                          n                                                  β      +      γ                        x                      n            −            k                                                            x                      n            −            l                                                  (                                                            x                                  n                  −                  k                                                                              +                                                                  x                                  n                  −                  l                                                                                        )            ,    n  =  0  ,  1  ,  2  ,  .  .  . where the parameters    α  ,  β  ,  γ  ,  δ  ∈  (  0  ,  ∞  ), while    m  ,  k  ,  l are positive integers, such that    m  <  k  <  l  . The initial conditions              x              −        m              ,  .  .  .  ,            x              −        k              ,  .  .  .  ,            x              −        l              ,  .  .  .  ,            x              −        1              ,  .  .  .  ,            x              0             are arbitrary positive real numbers. We will give some numerical examples to illustrate our results.}
}