Abstract
In this paper, we study the global behavior of the higher order nonlinear difference equation x n + 1 = β x n - k + 1 + γ x n - 2 k + 1 Bx n - k + 1 + Cx n - 2 k + 1 , n = 0 , 1 , … , where B, C and β, γ are positive, k ∈ {1, 2, 3, …}, and the initial conditions x −2 k+1 , … , x −1, x 0 are positive real numbers. We investigate the character of semicycles, periodicity, global stability and convergence to 2 k-cycle solutions of mentioned equation.
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