<p>It is widely acknowledged that the challenging Schrödingerequation may be understood as a dynamical system and a PDE. It constitutes a strong prototyping link between the two concepts. Related studies are already growing from theoretical and numerical perspectives. In the special nonlinear model, exact solutions remain complex tasks, especially with the appearance of coupled systems of NLS type proved more coherent in modeling many phenomena from different fields. In this paper, the steady-state solution of a dynamical NLS system is considered for higher dimensions. The nonlinearities are composed of cubic-superlinear correlated powers. Radially symmetric solutions are classified for the steady-state aspect, provided with uniqueness and existence results. In addition, the possible chaotic behavior is studied by investigating and simulating some discrete cases of the NLS dynamical system. These simulations opened the path for investigating the fractal structure of the attractors issued from these chaotic dynamical systems.</p>