Introduction. In the last quarter of the 20th century, the nature of global demo
graphic and economic development began to change rapidly: the continuously accel
erating growth of the main characteristics that had taken place over the previous two
hundred years was replaced by their sharp deceleration. The article presents the pre
liminary results of research on mathematical modeling and forecasting of world
7dynamics, aimed at analyzing observed trends and carried out within the framework
of the Russian Science Foundation project No. 20 61 46004 “World development
and ‘limits to growth’ in the 21st century: modeling and forecasting” (supervisor —
academician V.A. Sadovnichy).
Materials and methods. During the research, a cognitive scheme of the interac
tion of various spheres of life at different stages of historical development was formed,
basic dynamic equations were proposed that reflect these interactions, and a modi
fication of these equations was substantiated in relation to different historical eras.
For each historical epoch, based on the analysis of the corresponding system of equa
tions, a phase portrait was determined and its features were analyzed. Based on this
analysis, conclusions were drawn about the patterns of world development in the pe
riod under review.
Results of the study. The results of mathematical modeling have shown that hu
manity is currently moving into a fundamentally new phase of historical develop
ment, when the old economic and social technologies (liberal capitalism, classical so
cialism) no longer work. There is a transition of human society to a new phase state,
the shape of which has not yet been determined. Under these conditions, we are not
talking about forecasting, but about designing the future in new historical conditions.
The struggle of world projects begins. The project that is more successful will win.
The analysis of these projects was carried out.
Discussion. The materials of the article reflect the view of Russian scientists
on the cardinal changes taking place in the world in recent decades, based on mo
deling long term (lasting hundreds and thousands of years) macrosocial processes.
An analysis of options for further world development is made. Analysis and modeling
have shown that the interaction in the “society—nature” system will depend on
the type of social interactions that will be formed in the future society.
Conclusion. On the basis of the analysis carried out, an alternative project of
the future W society (with the conditional name “World organism”) is proposed,
based on the primacy of the principles of cooperation over the principles of compe
tition, Russia can and should formulate. If this project is implemented, as mathema
tical modeling shows, it is possible to solve global problems related to ecology, global
warming, and energy. This global project will make it possible to implement the ideas
of prominent Russian humanist scientists on the formation of a fundamentally new
integrative noospheric society at a new stage of historical development, the path to
which goes through the partnership of civilizations.
L.E. Grinin, N.O. Kovaleva, A.I. Andreev, S.E. Bilyuga, A.L. Grinin, O.I. Davy
dova, D.M. Musieva, were also intensely engaged in the research, who by right should
be considered as co authors of this article.
Key words: modeling, forecasting, global processes, growth limits, world development forecast.