On dynamics and solution expressions of a three dimensional nonlinear difference equations system - Al-Rakhami, Faiza; Elsayed, E (Journal of Innovative Applied Mathematics and Computational Sciences, 2023)
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.