  This monograph presents a geometric modeling method nonlinear dynamical
systems from experimental data . basis method is a qualitative approach to the
analysis of linear models and construction of the symmetry groups of attractors
of dynamical systems with controls . A theoretical study including the central
theorem manifold defining conditions of existence of the class in question
models in the local area , taking into account the group properties ,
estimation algorithms invariant characteristics , methods of constructing
models and identifiable description of the results obtained using the method
for simulation -driven engineering processes . included two application is the
development of the proposed approach : identification of groups symmetries on
the phase portraits of dynamical systems and the method of constructing neural
network predictive models
