On dynamics and solution expressions of a three dimensional nonlinear difference equations system

Abstract

 In this paper, we construct the solution expressions of fourth order nonlinear difference systems

Φ_n+1       =                   Φn−2Ψn−3                       ,

        α + Ψn (±1 ± Γn−1Φn−2Ψn−3)

Ψ_n+1       =                   Ψn−2Γn−3                        ,

        δ + Γn (±1 ± Φn−1Ψn−2Γn−3)

Γ_n+1        =                   Γn−2Φn−3                        ,

        γ + Φn (±1 ± Ψn−1Γn−2Φn−3)

where α, δ and γ are arbitrary real numbers. Furthermore, the solution’s qualitative behavior is explored, such as local stability and boundedness. In some cases, system has periodic solutions. Finally, we provide numerical examples to support our conclusions.