Explicit Solutions of a Three-dimensional System of Nonlinear Difference Equations

Abstract

I n this paper, we show that the system of difference equations 1 11 0 , , , N , 111 n n nn nn n nn n n n n n n xy yz zx xyz n xy yz zx + ++ + ++ = = = ∈ +++ where the initial values xyz , , are real numbers, are solvable in explicit form via some changes of variables and tricks. Also, we determine the forbidden set of the initial values xyz , , for the above mentioned system and investigate asymptotic behavior of the well-defined solutions by using these explicit formulas