Global attractivity and periodic character of difference equation of order four (Q1925526)

Summary: We investigate the global convergence result, boundedness, and periodicity of solutions of the recursive sequence \(x_{n+1} = ax_n + ((bx_{n-1} + cx_{n-2} + dx_{n-3})/(\alpha x_{n-1} + \beta x_{n-2} + \gamma x_{n-3})), n = 0, 1, \dots\), where the parameters \(a, b, c, d, \alpha, \beta\), and \(\gamma\) are positive real numbers and the initial conditions \(x_{-3}, x_{-2}, x_{-1}\), and \(x_0\) are positive real numbers.