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International Conference on Complex Systems (ICCS2006)

Nonassociative algebraic structures and complex dynamical systems

Yuriy Gulak
Center for Structures in Extreme Environments, Rutgers Unive

Haym Benaroya
Mechanical and Aerospace Engineering, Rutgers University

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     Last modified: May 30, 2006

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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