NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2005, Vol.8, No.1, pp.68-73


Entropy and Chaotical Properties of Social Hierarchical Dynamical Systems.
I.A. Miklashevich

We investigate chaotical properties of hierarchical dynamical system applying special social system description. We are basing on the method of dynamical entropy computing by finding appropriate iterated function system (IFS) with the same entropy. It is shown that for an IFS which fulfils some additional assumptions there exists a unique invariant probability measure , in general fractal one. The exact value of is the limit of the sequence of and the IFS generated the hyperreal number. The Kolmogorov and Sinai entropy (KSE) of IFS is the exact value of hyperreal number, and the Rényi entropy is equal to the topological entropy. The KSE is the limit case of Rényi entropy and the halo of monad can be represented as the difference between these entropies. For two - dimensional Markov processes the halo of monad is represented as hypersphere in index space. For a social hierarchical dynamical system the increasing of indeterminacy by the system growth is found. This increasing is a function of the operators of hierarchical movements and .
Key words: dynamical system, iterated function system, hierarchy, non-standard analysis, entropy, monad, haziness, indeterminacy

Full text:  Acrobat PDF  (146KB)   PostScript (239KB)   PostScript.gz (114KB)



ContentsJournal Home Page

Copyright © Nonlinear Phenomena in Complex Systems. Last updated: March 22, 2005