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 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.

Keywords

• Rational difference equations
• solution of system of difference equation
• periodic solution
• recursive sequences
• local stability