Dynamics of a high-order rational difference equation

Abstract

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.