  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.
