Qualitative Analysis of a Three-Dimensional Exponential Difference System With Delay

In this paper, we investigate the qualitative properties of a nonlinear exponential difference system for a three-dimensional system with delay.In particular, we study the boundedness, persistence, and invariant sets of positive solutions of the following system:, where all parameters and initial conditions are positive.Sufficient conditions ensuring boundedness, persistence, and the existence of positively invariant regions are established.Furthermore, under suitable sufficient conditions, the existence and uniqueness of the positive equilibrium point are established using fixed-point arguments.