On the Global Behavior of the Rational System x_n+1 = α_1 x_n + y_n AND y_n+1 = α_2 + β_2 x_n + y_n y_n - Grove, E. A.; Hadley, D.; Lapierre, E.; Schultz, S.W. (Sarajevo Journal of Mathematics, 2024)
We investigate the system of rational difference equations in the title, where the parameters and the initial conditions are positive real numbers. We show that the system is permanent and has a unique positive equilibrium which is locally asymptotically stable. We also find sufficient conditions to insure that the unique positive equilibrium is globally asymptotically stable. 2000 Mathematics Subject Classification. 39A10, 39A11