Global behavior of a three-dimensional system of difference equations of order three

Abstract

In this paper, we investigate the global behavior of the positive solutions of the system of di¤erence equations u n+1 = 1 u n 1 1 + 1 v p n 2 ; v n+1 = 2 v n 1 2 + 2 w q n 2 ; w n+1 = 3 w n 1 3 + 3 u r n 2 for n 2 N 0 where the initial conditions u i ; v i ; w i (i = 0; 1; 2) are nonnegative real numbers and the parameters j ; j ; j (j = 1; 2; 3) and p; q; r are positive real numbers, by extending some results in the literature.

On a System of k-Difference Equations of Order Three

“…is paper extends the results of studies in the references [1][2][3]. at is to say, if we take k � 1, then system (4) reduces equation ( 1).…”

“…Example 2. If k � 4, x (1) n � x n , x (2) n � y n , x (3) n � z n , x (4) n � p n , r 1 � 2, r 2 � 3, r 3 � 4, and r 4 � 5 in system (5), we obtain the following system:…”

“…where the parameters and initial conditions are positive real numbers. Tollu and Yalcinkaya [3] dealt with the dynamical behavior of the positive solutions for the following three-dimensional system of rational difference equations:…”

“…In the present paper, we investigate the global behavior of the positive solutions of the k-dimensional system of difference equations: u (1) n+1 � α 1 u (1) n−1 β 1 + c 1 u (2) n−2 r 1 , u (2) n+1 � α 2 u (2) n−1 β 2 + c 2 u (3) n−2 r 2 , . .…”

On a general homogeneous three-dimensional system of difference equations

“…In the literature there are many studies on difference equations defined by homogeneous functions, see for instance [1,2,5,7,11,16]. Noting that also a lot of studies are devoted to various models of difference equations and systems, not necessary defined by homogeneous functions, see for example [4,9,10,12,14,18,19,20,21,22,24,25,26,27,28,29].…”