Abstract
This work is devoted to present a study of the class of the difference equations x(n+1) = x(n-2q+1)/A + Bx(n-2q+1)x(n-q+1), q = 1,2, ... with arbitrary initial data, where A and B are arbitrary parameters, and q is an arbitrary nonnegative integer. We present a detailed investigation of the behavior of the solution, including their dependence on parameters and initial conditions. Local and global stabilities of the equilibrium points are discussed. The existence of a periodic solution is studied. Numerical simulations are given to assure the correctness of the analytical results. This study improves and surpasses studies of several forms of difference equations that have been investigated earlier by many researchers. (c) 2020 The Authors. Published by IASE. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).