On the asymptotic behavior of a system of two rational difference equations

The subject of this paper is a system of two rational type difference equations with constant coefficients in the form: {x1(n+1)=ax1k(n)+bx2(n)x2(n+1)=ax1k2(n), where aa, b∈Rb∈R, k∈N={1,2,…}k∈N={1,2,…}, n∈N0n∈N0, N0={0,1,2,…}N0={0,1,2,…}. The asymptotic behavior of the solutions and the phase portrait are described. Moreover, an attractor is investigated.