A solvable three dimensional system of difference equations of second order with arbitrary powers

Abstract

The solvability in a closed form of the following three-dimensional system of difference equations of second order with arbitrary powers
xn+1=ynyqn−1xpn(a+bynyqn−1),yn+1=znzrn−1yqn(c+dznzrn−1),zn+1=xnxpn−1zrn(h+kxnxpn−1),n,p,q,r∈N0xn+1=ynyn−1qxnp(a+bynyn−1q),yn+1=znzn−1rynq(c+dznzn−1r),zn+1=xnxn−1pznr(h+kxnxn−1p),n,p,q,r∈N0
where the initial values x_{_i}, y_{_i}, z_{_i}, i=0,1 are non-zero real numbers and the parameters a,b,c,d,h, are real numbers, will be the subject of the present work. We will also provide the behavior of the solutions of some particular cases of our system.