On the Trichotomy Character of xn+1 = α+γX n-1/A+BXn+Xn-2

Abstract

We investigate the global stability, the periodic character, and the boundedness nature of the solutions of the difference equation xn+1 = α+γXn-1/A+BXn+xn-2, n = 0, 1, . . . where the parameters α, γ, A, B and the initial conditions x -2, x-1, x0 are non-negative real numbers. We show that the solutions of the equation exhibit a trichotomy character which depends upon whether γ is less than A, equal to A, or greater than A.