Qualitative behavior of an anti-competitive system of third-order rational difference equations

Abstract

In this paper, our aim is to study the equilibrium points, local asymptotic stability, global behavior of an equilibrium points and rate of convergence of an anti-competitive system of third-order rational difference equations of the form: xn+1=ayn-2/[b+rxnxn-1xn-2], yn+1=cxn-2/[d+hynyn-1yn-2], n=0,1,2,..., where the parameters a, b, c, d, r, h and initial conditions x0, x-1, x-2, y0, y-1, y-2 are positive real numbers. Some numerical examples are given to verify our theoretical results.

Keywords

• rational difference equations
• stability
• global character
• rate of convergence