Dynamics of a Higher-Order Nonlinear Difference Equation

Dynamics of a Higher Order Nonlinear Difference Equation

We consider the higher-order nonlinear difference equation xn 1 α xn / A Bxn xn−k , n 0, 1, . . ., where parameters are positive real numbers and initial conditions x−k, . . . , x0 are nonnegative real numbers, k ≥ 2. We investigate the periodic character, the invariant intervals, and the global asymptotic stability of all positive solutions of the abovementioned equation. We show that the uniq...

On a Higher-Order Nonlinear Difference Equation

and Applied Analysis 3 After k steps we obtain the following formula xn A ⎛ ⎝ A x r/p n−k ⎛ ⎝ A x r/p2 n−k x r/p n−k−1 ⎛ ⎝ A x r/p3 n−k x r/p2 n−k−1x r/p n−k−2

Solvability of a Higher-Order Nonlinear Neutral Delay Difference Equation

The existence of bounded nonoscillatory solutions of a higher-order nonlinear neutral delay difference equationΔ akn · · ·Δ a2nΔ a1nΔ xn bnxn−d f n, xn−r1n , xn−r2n , . . . , xn−rsn 0, n ≥ n0, where n0 ≥ 0, d > 0, k > 0, and s > 0 are integers, {ain}n≥n0 i 1, 2, . . . , k and {bn}n≥n0 are real sequences, ⋃s j 1{rjn}n≥n0 ⊆ Z, and f : {n : n ≥ n0} × R → R is a mapping, is studied. Some sufficient...

Global attractivity of a higher-order nonlinear difference equation

In this paper, we investigate the global attractivity of negative solutions of the nonlinear difference equation xn+1 = 1− xn−k A + xn , n = 0, 1, . . . , where A ∈ (−∞, 0), k is a positive integer and initial conditions x−k, · · · , x0 are arbitrary real numbers. We show that the unique negative equilibrium of abovementioned equation is a global attractor with a basin under certain conditions....

Dynamics of a System of Rational Higher-Order Difference Equation