Global Asymptotic Stability of a Rational System - Lin-Xia Hu; Xiu-Mei Jia (Abstract and Applied Analysis)
The main goal of this paper is to investigate the global asymptotic behavior of the difference equation xn+1=β1xn/A1+yn, yn+1=β2xn+γ2yn/xn+yn, n=0,1,2,… with β1,β2,γ2,A1∈(0,∞) and the initial value (x0,y0)∈[0,∞)×[0,∞) such that x0+y0≠0. The major conclusion shows that, in the case where γ2<β2, if the unique positive equilibrium (x-,y-) exists, then it is globally asymptotically stable.