Dynamical study of the class of difference equation Xn+1= Xn-2q+1/A+BXn-2qXn-q+1

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 and are arbitrary parameters, and 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.