On the solutions of some system of difference equations and behaviors of their solutions

This study consists of six chapters. In the first chapter, the general information about the difference equations is given. In the second chapter, studies in literatüre on difference equations and systems of difference equations are mentioned. Also, some definitions and theorems are given about difference equations and system of difference equations. In the third chapter, system of difference equation x_{n}=\frac{x_{n-k}y_{n-l}}{bx_{n-k}+ay_{n-k-l}}, \ y_{n}=\frac{y_{n-k}z_{n-l}}{dy_{n-k}+cz_{n-k-l}}, \ z_{n}=\frac{z_{n-k}x_{n-l}}{fz_{n-k}+ex_{n-k-l}}, \ n\in \mathbb{N}_{0} is defined, its solutions are obtained and the asymptotic behavior of the solutions is investigated. In the fourth chapter, solvability of system of difference equation x_{n+1}=y_{n}^{\alpha}z_{n-1}^{\beta}, \ y_{n+1}=z_{n}^{\gamma}t_{n-1}^{\delta}, \ z_{n+1}=t_{n}^{\epsilon}x_{n-1}^{\mu}, \ t_{n+1}=x_{n}^{\xi}y_{n-1}^{\rho}, \ n\in \mathbb{N}_{0} is shown and general solution is obtained for some special cases. In the fifth chpater, numerical examples supporting the obtained properties related to the system of difference equations studied in the third chapter are given. In the sixth chapter, results and discussions are given.