@article{Sun2023, 
author = {Taixiang Sun and Guangwang Su and Bin Qin and Caihong Han},
title = {Global behavior of a max-type system of difference equations of the second order with four variables and period-two parameters},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {10},
pages = {23941-23952},
keywords = {max-type system of difference equations, solution, eventual periodicity},
url = {https://www.sciopen.com/article/10.3934/math.20231220},
doi = {10.3934/math.20231220},
abstract = {In this paper, we study global behavior of the following max-type system of difference equations of the second order with four variables and period-two parameters         {                                        x                          n                                =          max                      {                                A            n                    ,                                    z                              n                −                1                                                    y                              n                −                2                                                          }                    ,                                y                          n                                =          max                      {                                B            n                    ,                                    w                              n                −                1                                                    x                              n                −                2                                                          }                    ,                                z                          n                                =          max                      {                                C            n                    ,                                    x                              n                −                1                                                    w                              n                −                2                                                          }                    ,                                w                          n                                =          max                      {                                D            n                    ,                                    y                              n                −                1                                                    z                              n                −                2                                                          }                    ,                                        n  ∈  {  0  ,  1  ,  2  ,  ⋯  }  ,where        A    n    ,      B    n    ,      C    n    ,      D    n    ∈  (  0  ,  +  ∞  ) are periodic sequences with period 2 and the initial values        x          −      i        ,      y          −      i        ,      z          −      i        ,      w          −      i        ∈  (  0  ,  +  ∞  )    (  1  ≤  i  ≤  2  ). We show that if    min  {      A    0        C    1    ,      B    0        D    1    ,      A    1        C    0    ,      B    1        D    0    }  <  1, then this system has unbounded solutions. Also, if    min  {      A    0        C    1    ,      B    0        D    1    ,      A    1        C    0    ,      B    1        D    0    }  ≥  1, then every solution of this system is eventually periodic with period    4.}
}