Abstract
In the present paper, we prove the boundedness of the positive solutions as well as local and global asymptotic stable of the equilibrium points of difference equations system in the second order
Un+1 = b(1)V(n) + c(1)V(n)U(n-1)/r + V-n + Un-1,
Vn+1 = b(2)U(n) + c2U(n)V(n-1)/r + U-n +/- Vn-1,
Furthermore, we study the solutions for three special cases of system. Numerical examples are provided to illustrate results.