Global dynamics of three anticompetitive systems of difference equations in the plane (Q1956112)

Summary: We investigate the global dynamics of several anticompetitive systems of rational difference equations which are special cases of general linear fractional system of the forms \(x_{n+1} = (\alpha_1 + \beta_1x_n + \gamma_1y_n)/(A_1 + B_1x_n + C_1y_n), y_{n+1} = (\alpha_2 + \beta_2x_n + \gamma_2y_n)/(A_2 + B_2x_n + C_2y_n), n = 0, 1, \dots\), where all parameters and the initial conditions \(x_0, y_0\) are arbitrary nonnegative numbers, such that both denominators are positive. We find the basins of attraction of all attractors of these systems.