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

### Abstract

In this paper, we show that the system of difference equations xn+1=(xn+yn)/(1+xnyn), yn+1=(yn+zn)/(1+ynzn), zn+1=(zn+xn)/(1+znxn); n =0,1,..., where the initial values x0, y0, z0 are positive real numbers, are solvable in explicit form via some changes of variables and tricks. Also, we determine the forbidden set of the initial values x0, y0, z0 for the above mentioned system and investigate asymptotic behavior of the well-defined solutions by using these explicit formulas.

**Keywords:**

Asymptotic behavior; Explicit solution; Forbidden set; Rational difference equation; System.

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### References

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*Hittite Journal of Science & Engineering*,

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