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We investigate global dynamics of the following systems of difference equations: { x n + 1 = b 1 x n 2 A 1 + y n 2 , y n + 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 at ∞. MSC:39A10, 39A30, 37E99, 37D10.

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