Dynamics of a high-order rational difference equation - Wang, Yanqin,; Tu, Qingwei,; Wang, Qiang,; Hu, Chao, (Utilitas Mathematica, 2012)
In this paper, we study the global behavior of the higher order nonlinear difference equation x n+1 = A+Bx n-k+1+Cx n-2k+1/α+βx n-k+1+γx n-2k+1, n = 0, 1, , where A, B, C and α, β, γ are positive, k ε{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, invariant intervals, global stability of the above mentioned equation.