The characteristics of a higher-order rational difference equation

Abstract: In this paper, we study the global behavior of the higher order nonlinear difference equationwhere A, B and α, β, γ are positive, k ∈{1,2,3,…}, and the initial conditions x −2k+1,…, x −1, x 0 are positive real numbers. We investigate the character of semicycles, periodicity, global stability and boundedness of above mentioned equation. [Copyright &y& Elsevier]