Analysis of coordinate and other transformations of models of dynamical systems by the reduction method

The issues of preserving dynamic properties when passing from a system of differential equations to another system obtained by a change of variables are considered, as well as issues of preserving the properties in the opposite direction. The possibilities of the reduction method, which was proposed earlier, in resolving these questions are demonstrated by the examples of such properties as stability, attraction, and dissipativity. Similar questions are investigated for the case when the second system is obtained by a way characteristic for the comparison method with vector Lyapunov functions. The application of one of the obtained dissipativity criteria to analyzing the nonlinear dynamics of a group of moving objects is considered.