Dynamics of a two-dimensional competitive system of rational difference equations with quadratic terms

We investigate global dynamics of the following systems of difference equations: {Xn+1 = b1x(n)(2)/A(1)+y(n)(2), Yn+1 = a(2)+c(2)y(n)(2) /x(n)(2), n = 0, 1, 2, ..., where the parameters b(1), a(2), A(1), c(2) are positive numbers and the initial condition y(0) is an arbitrary nonnegative number and x(0) is a positive number. We show that this system has rich dynamics which depends on the part of a parametric space. We find precisely the basins of attraction of all attractors including the points infinity.