AACIMP 2010 Summer School lecture by Alexander Makarenko. "Applied Mathematics" stream. "General Tasks and Problems of Modelling of Social Systems. Problems and Models in Sustainable Development" course. Part 3. More info at http://summerschool.ssa.org.ua

1. NEURAL NETWORKS
MODELS FOR LARGE
SOCIAL SYSTEMS
Professor Alexander S. MAKARENKO
Institute for Applied System Analysis at
National Technical University of Ukraine (KPI) , Kyiv, Ukraine,
Head of Applied Nonlinear Analysis Department
E-mail: makalex@i.com.ua

2. I. BAKGROUND FOR SOCIAL
SYSTEMS MODELING
Associative memory approach to large socio-
technical systems (Makarenko, 1992, 1998,
2001, 2003)
‘Patterns’
 The ‘pattern’ is the collection of elements and bonds between them at
any moment of time.
 Such description is useful as for environment as for the mental
structures of individuals (or agents in the models).
 Such ‘geometrical’ description may be transformed in pure ‘logical’ or
sometimes ‘linguistic’ description

3. Pattern of system in given time
moment

4. Some facts on social systems
 Firstly in complex system dynamic there exist some
global structures (for example formations or civilisations).
 The socio-technical system as the rule changes in the
frame of such structures.
 Secondly, alternation in elements state frequently is
determined by the influence of some environment. This
can be described by some mean field approach .
 There are many interrelations between the elements of
complex systems (and not only in social but also in
natural systems).

5. Examples of the properties
 There are many sub-processes in such system – communicational, political, social, cultural
and so on.
 The system can go from one global structure to another by two ways: evolutionary or by
revolution.
 Revolution can be described by fast rupture of bonds and may be unpredictable.
 Evolutionary way is long and demands patience.
 Yet on such global level there are phenomena of life- cycle type.
 For example, the change of social formation may be considered as the change of
"patterns" in such models.
 Branch of industry may be considered as union of producers, consumers and mediators.
 These relations have the same properties as the subjects of global model:
 The bonds are build evolutionary, all structure of industry branch is rather stable

6. Internal representation of external
world and mental properties

7. Real pattern of the world and
‘known mental representation

8. General formula for the model with
associative memory with memory
si (t 1) f i ({si (t )},{si (t 1)},...,{J ij (t 1)},..., b).

9. Simplest example (Hopfield type
model)
si (t 1) sign(hi );

10. Simplest example (Hopfield type
model)
sign(W ) { 1....if ...W 0; 1...if ...W 0}.

11. ‘Landscape’ of potential function

12. 1D ‘presentation’ of potential
landscape

13. SOCIETY AS THE NETWORKS
OF INDIVIDUALS AND OTHER
COMPONENTS

14. II. Anticipation and possible
consequences in models
Anticipatory property (R.Rosen, D.Dubois) for social systems and
scenarios
 Now it became known that one of very interesting for understanding the
society property is anticipating.
 Weak anticipation – the system has the model for forecast the future
 Strong anticipation – the future state isn’t known but influence on transition
in time
 The main essential new property is the possibility of multi-valued solution
(that is many values of solution for some moments of time and initial
conditions). This may be interpreted as the possibility of many scenarios of
development for real social systems.
 The second key issue is connected to property that the real social system
has single realization of historical way (trajectory). So the social system as
the whole makes the choice of the own trajectory at any moment of time.
 Local SD processes usually are with weak anticipation
 Global SD processes are strongly anticipative

15. General formula for the model with
ANTICIPATION
S i (t 1) Gi ({si (t )},...,{si (t g (i ))}, R ),

16. Scenarios and decisions
Multi-valued solutions and single trajectory
X
0 1 2 3 t

17. REFERENCES
 Dubois Daniel, 1998. Introduction to computing Anticipatory
Systems. nternational Journal of Computing Anticipatory Systems,
(Liege), Vol. 2, pp.3-14.
 Haykin S., 1994. Neural Networks: Comprehensive Foundations.
MacMillan: N.Y.,
 Makarenko A., 1998. New Neuronet Models of Global Socio-
Economical Processes. In 'Gaming /Simulation for Policy
Development and Organisational Change' (J.Geurts, C.Joldersma,
E.Roelofs eds) , Tillburg University Press. 133- 138,
 Makarenko A., 2003. Sustainable Development and Risk Evaluation:
Challenges and Possible new Methodologies, In. Risk Science and
Sustainability: Science for Reduction of Risk and Sustainable
Development of Society, eds. T.Beer, A.Izmail- Zade, Kluwer AP,
Dordrecht, p. 87- 100.
 Zgurovsky M., Gvishiani A., 2008. Sustainable Development Global:
Simulation. Quality of Life and Security of the World Population
(2005 – 2007/ 2008). Kyiv: NTUU ‘KPI’, POLITECHNIKA. 336 p.