What Future Expects Humanity After the Demographic Transition Time?
  The variant of phenomenological theory of humankind future existence after time of demographic transition based on treating the time of demographic transition as a point of phase transition and taking into account an appearing of the new phase of mankind is proposed. The theory based on physical phenomenological theories of phase transitions and classical equations for system predatory-preys for two phases of mankind, take into account assumption about a multifractal nature of the set of number of people in temporal axis and contains control parameters. The theory includes scenario of destroying of existent now human population by new phase of humanity and scenario of old and new phases co-existence. In particular cases when the new phase of mankind is absent the equations of theory may be formulated as equations of Kapitza, Foerster, Hoerner, Kobelev and Nugaeva, Johansen and Sornette phenomenological theories of growth of mankind. 
L.Ya.Kobelev, L.L.Nugaeva