Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2005-09-05
Nonlinear Sciences
Adaptation and Self-Organizing Systems
8 pages, 4 figures, index corrected, minor changes mainly of stylistic character
Scientific paper
In the paper we present a description of complex systems in terms of self-organization processes of prime integer relations. A prime integer relation is an indivisible element made up of integers as the basic constituents following a single organizing principle. The prime integer relations control correlation structures of complex systems and may describe complex systems in a strong scale covariant form. It is possible to geometrize the prime integer relations as two-dimensional patterns and isomorphically express the self-organization processes through transformations of the geometric patterns. As a result, prime integer relations can be measured by corresponding geometric patterns specifying the dynamics of complex systems. Determined by arithmetic only, the self-organization processes of prime integer relations can describe complex systems by information not requiring further explanations. This gives the possibility to develop an irreducible theory of complex systems.
Korotkikh Galina
Korotkikh Victor
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