Behaviour of a three dimensional system of rational difference equations

In this study, the properties of a three-dimensional system of difference equations are investigated, with particular emphasis on boundedness, persistence, and the conditions for the existence and uniqueness of a positive equilibrium. Additionally, the local and global dynamics around the positive equilibrium point are analyzed, and the rate of convergence of positive solutions examined. The system under consideration is given by pn+1=γ1+δ1pn−1η1+ζ1qn, qn+1=γ2+δ2qn−1η2+ζ2rn,rn+1=γ3+δ3rn−1η3+ζ3pn,n∈N0, where the parameters γl, δl, ηl, ζl for l∈{1,2,3} and the initial conditions p−1,p0, q−1,q0, r−1,r0 are positive real numbers.