Global Behavior of a Discrete Anticompetitive System in the Plane

Abstract

The main goal of this paper is to investigate the global asymptotic behavior of the difference systemxn+1=γ1yn/A1+xn,  yn+1=β2xn/B2+yn,  n=0,1,2,….withγ1,β2,A1,B2∈(0,∞)and the initial condition(x0,y0)∈[0,∞)×[0,∞). We obtain some global attractivity results of this system for different values of the parameters, which answer the open problem proposed in “Rational systems in the plane, J. Difference Equ. Appl. 15 (2009), 303-323”.