Dynamics of a System of Rational Higher-Order Difference Equation

Banyat Sroysang

doi:10.1155/2013/179401

Abstract

We focus on a system of a rational -order difference equation , , , where . We investigate the dynamical behavior of positive solution for the system.

Highlights

In 2011, Kurbanli et al [1] studied the behavior of positive solutions of the system of rational difference equations xn+1 = xn−1 ynxn−1 + (1) yn+1 yn−1 xnyn−1 +1, where the initial conditions are arbitrary nonnegative real numbers.In the same year, Kurbanli [2] studied the behavior of solutions of the system of rational difference equations xn+1xn−1, ynxn−1 − 1 yn+1yn−1, xnyn−1 − 1 (2)
We focus on a system of a rational m-order difference equation xn+1 =/(A + ynyn−1 ⋅ ⋅ ⋅ yn−m+1), yn+1 =/(B + xnxn−1 ⋅ ⋅ ⋅ xn−m+1), n = 0, 1, . . ., where A, B, x0, x−1, . . . , x−m+1, y0, y−1, . . . , y−m+1 ∈ (0, ∞)
We investigate the dynamical behavior of positive solution for the system

Summary

Introduction

We focus on a system of a rational m-order difference equation xn+1 = (xn−m+1)/(A + ynyn−1 ⋅ ⋅ ⋅ yn−m+1), yn+1 = (yn−m+1)/(B + xnxn−1 ⋅ ⋅ ⋅ xn−m+1), n = 0, 1, . In 2011, Kurbanli et al [1] studied the behavior of positive solutions of the system of rational difference equations xn+1 Kurbanli [2] studied the behavior of solutions of the system of rational difference equations xn+1 Kurbanli [3] studied the behavior of the solutions of the difference equation system xn+1

Results

Conclusion