There are interesting ways of categorically mapping the structure, behavior and evolution (morphisms) of dynamical systems ala Steven Strogatz in "Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering", by Perseus Publishing. This has been detailed by Category Theory (CT - Eilenberg, Mac Lane, Lawvere, among many more) and the use of functors - a programmatic analog affecting state evolutions.
Rather than the set-theoretic approach, with it's limitations of First Order Logic, CT provides a more accurate logical / analytical framework in which to understand complex, dynamical systems, and categorize (or classify) their patterns of change.
Curious. This particular technique seems grossly under-utilized in Complex Systems Theory, and in understanding complex, dynamical systems, their processes, growth and evolution. Furthermore, it seems that these known techniques are actually ignored.
If someone has a good explanation for this phenomenon, I'd sure like to hear it - or am I not looking for exemplars in the right places?
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