Investigating dynamical behaviors of the difference equation X n+1 = Cxn−5 / A+Bxn−2xn−5

In this work, we investigate the dynamical behaviors of the rational difference equation X n+1 = Cxn−5 / A+Bxn−2xn−5 with arbitrary initial conditions, where A, B, and C are arbitrary constants. A general solution is obtained. Asymptotic behavior and asymptotic stability of the equilibrium points are investigated. The existence of the periodic solutions is discussed. Numerical simulations are carried out to verify the analytical results.