The Exact Nonlinear Dynamics. New Bifurcation Groups with Chaos and Rare Attractors

New nonlinear models which allows to obtain exact periodic, quasi-periodic and chaotic attractors and transients processes, are proposed. The idea of “exact” models has its corner-stone in description of restoring, damping and excitation forces only by constant forces on each its linear sub-system. Examples with a system with one potential well, two potential wells and pendulum systems are discussed. We suppose that it will be possible finding the exact simple analytical formulae for periodic, quasi-periodic and chaotic dynamics in different nonlinear models.