On the stability analysis of the second-order three-dimensional difference equation system

This thesis consists of five sections. In the first section, basic definitions and theorems related to difference equations and systems of difference equations are presented. In the second section, some studies on difference equations and difference equation systems are included. In the third section, a three-dimensional second-order difference equation system is considered. The boundedness and persistence of the solutions of this system, the global asymptotic stability of the positive equilibrium point, and the rate of convergence are investigated. In the fourth section, numerical examples are given to verify the theoretical results obtained regarding the difference equation system discussed in the third section. In the fifth section, conclusions and suggestions are provided. Keywords: Difference equations, System of difference equations, Global asymptotic stability, Rate of convergence