Generation of the chaos in hierarchical systems.
Belarusian national technical university
Last modified: March 29, 2006
In hierarchical representation in general case the system development realizing in such a way that the highest level properties occur not to be an elementary sum of lower levels properties but acquire a basically new character. This is a natural realization of the well-known philosophical principle - the whole is more than the simple sum of all its parts. These novel properties can not
be expressed in terms and concepts of lower levels but must be expressed in terms of given level and upper levels, which are unknown yet in general. It means that the system uncertainty
(haziness) is the immanent property of any complex system.
The mathematical structure of operators describing movements in hierarchical system state space is proposed. Taking into account the description of social systems as a hierarchical movement the hyperreal character of these operators for social system modelling is established. The law of superposition of the operators is obtained. The origin of second order uncertainty due to the movement through hierarchical state space is studied and interpreted in terms of social groups dynamics.
Proposed non-standard extension of sociodynamics makes it possible to represent human free
will as a mathematical object The entropy of the hierarchical system can be found. On the base of entropy calculation the optimal trajectory of social system evolution can be found and minimal control influence can be build.