|InterJournal Complex Systems, 1807
|Manuscript Number: |
Submission Date: 2006
|Nonassociative algebraic structures and complex dynamical systems|
Because of the lack of a unifying framework, complex phenomena are often treated with very ad hoc methods (from a traditional mathematical viewpoint). We, however, demonstrate that complex systems such as elementary cellular automata, nonlinear (quadratic) differential and difference equations can be considered as dynamical systems on the appropriate nonassociative algebraic structures. Expressing the low-level interactions of components in different systems as algebraic operations allows one to relate the properties of their emergent large scale behavior to the properties of the corresponding algebras. We discuss the special role of nonassociativity and consequent fundamental limitations of formal algorithmic approaches to the studies of complex systems.
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