Stability analysis of a three-dimensional system of difference equations with quadratic terms

Abstract This study is involved with a class of three-dimensional system of difference equations incorporating quadratic term, which naturally extends and improve several results in the literature. Firstly, we demonstrate the existence of fixed points, the boundedness, persistence and invariance of positive solution of the mentioned system. Later, for this system, we give the global asymptotic stability at fixed point and the rate of convergence result which play an important role in the discrete dynamical systems. And lastly, some numerical examples are given to validate the effectiveness and feasibility of the theoretical findings.