Dynamics of a three-dimensional system of difference equations with exponents

The studies carried out in this thesis are presented in five main sections. In the first section, the aim of thesis are given. In the second section, the literature review on difference equations with exponential type and system of difference equations are given. Also general definitions and theorems about difference equations and systems of difference equations are given. In the third section, the boundedness and persistence of the solutions of three-dimensional difference equations with exponents, the convergence to positive equilibrium point of positive solutions and asymptotic behaviour of positive solutions of the following system of difference equations x_{n+1}=\alpha_{1}+ae^{-x_{n-1}}+by_{n}e^{-y_{n-1}} y_{n+1}=\alpha_{2}+ce^{-y_{n-1}}+dz_{n}e^{-z_{n-1}} z_{n+1}=\alpha_{3}+fe^{-z_{n-1}}+gx_{n}e^{-x_{n-1}}, n\in\{N_{0}\}, where the parameters \alpha_{1}, \alpha_{2}, \alpha_{3}, a, b, c, d, f, g and initial conditions x_{-i}, y_{-i}, z_{-i} for i\in\{0,1\} are positive real numbers, are examined. In the fourth section, numerical examples supporting the theoretical studies given in the third section are given. In the fifth section, the results and discussions are given.