NEURAL NETWORKS

MODELS FOR LARGE

SOCIAL SYSTEMS

Professor Alexander S. MAKARENKO

Institute for Applied System Analysis atNational Technical University of Ukraine (KPI) , Kyiv, Ukraine, Head of Applied Nonlinear Analysis DepartmentE-mail: makalex@i.com.ua

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

Pattern of system in given time

moment

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).

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

Internal representation of external

world and mental properties

Real pattern of the world and

‘known mental representation

General formula for the model with

associative memory with memory

).)},...,1({)},...,1({)},(({)1( btJtstsfts ijiiii

Simplest example (Hopfield type

model)

);()1( ii hsignts

Simplest example (Hopfield type

model)

}.0......1;0.......1{)( WifWifWsign

‘Landscape’ of potential function

1D ‘presentation’ of potential

landscape

SOCIETY AS THE NETWORKS

OF INDIVIDUALS AND OTHER

COMPONENTS

II. Anticipation and possible

consequences in modelsAnticipatory 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

General formula for the model with

ANTICIPATION

),))},(({)},...,(({)1( RigtstsGtS iiii

Scenarios and decisions

Multi-valued solutions and single trajectory

1 2 3 t

X

0

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.