On the Trichotomy Character of

Abstract

Abstract We investigate the global stability, the periodic character, and the boundedness nature of the solutions of the difference equation where the parameters α, γ, A, B and the initial conditions x -2, x -1, x 0 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. Keywords: BoundednessDifference equationGlobal attractorPeriodic solutionPeriod-two trichotomyTrichotomy character39A1039A11