Attractors of 3D Systems in Basic Models of Mechanics

The theorems (statements) on the existence of attractor are proved. A generalized Shilnikov theorem is formulated. In the expression for the saddle of a homoclinic loop, it includes an additional term that has a qualitative value in the formation of a strange attractor. A bifurcation program for the synchronization of 3D coupled identical generators is considered. The cause of new motions appearing in coupled generators is established.