Qualitative behavior of rational difference equation of big order (Q1956066)

Summary: We investigate the global convergence, boundedness, and periodicity of solutions of the recursive sequence \(x_{n+1} = (ax_{n-l} + bx_{n-x})/(c + dx_{n-l}x_{n-k})\), \(n = 0, 1, \dots\), where the parameters \(a, b, c\) and \(d\) are positive real numbers, and the initial conditions \(x_{-t}, x_{-t+1}, \dots, x_{-1}\) and \(x_0\) are positive real numbers where \(t = \max\{k, l\}\).