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In this paper, we construct the solution expressions of fourth order nonlinear difference systems
Φn+1 = Φn−2Ψn−3 ,
α + Ψn (±1 ± Γn−1Φn−2Ψn−3)
Ψn+1 = Ψn−2Γn−3 ,
δ + Γn (±1 ± Φn−1Ψn−2Γn−3)
Γn+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.
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