This article is talking about the study constructive method of structural identification systems with chaotic dynamics. It is shown that the reconstructed attractors are a source of information not only about the dynamics but also on the basis of the attractors which can be identified and the mere sight of models. It is known that the knowledge of the symmetry group allows you to specify the form of a minimal system. Forming a group transformation can be found in the reconstructed attractor. The affine system as the basic model is selected. Type of a nonlinear system is the subject of calculations. A theoretical analysis is performed and proof of the possibility of constructing models in the central invariant manifold reduced. This developed algorithm for determining the observed symmetry in the attractor. The results of identification used in real systems are an application.