Global behavior of a higher order difference equation

Abstract

ABSTRACT. The aim of this paper is to investigate the global stability and periodic nature of the positive solutions of the difference equationwhere A, B are nonnegative real numbers, C, D > 0 and l, k are nonnegative integers such that l ≤ k.

On the solutions of a system of (2p+1) difference equations of higher order

“…In this section we study the global stability character of the solutions of system (1.9). It is easy to show that (1.9) has a unique real positive equilibrium point given by E = x (1) , x (2) , . .…”

“…Let k = 1 and p = 2 in system (1.9), then we obtain the system Example 2. Let k = 3 and p = 3 in system (1.9), then we obtain the system (n) X (3) (n) X (4) (n) X (1) (n) X (2) (n) X…”

On forbidden sets

“…The case b = 1 and a, c > 0 in (13) was developed in [38], while a = ±1, b = 1 and c = −1 is in [4]. See also [1,3] for a > 0 and bc < 0.…”

Global behavior of a third order difference equation with quadratic term

“…Recently, there has been a great interest in studying properties of nonlinear and rational difference equations (see [1,[4][5][6][7][8][9][10] and the references therein).…”