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Article overview
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A contraction based, singular perturbation approach to near-decomposability in complex systems | Gabriel D. Bousquet
; Jean-Jacques E. Slotine
; | Date: |
28 Dec 2015 | Abstract: | We revisit the classical concept of near-decomposability in complex systems,
introduced by Herbert Simon in his foundational article The Architecture of
Complexity, by developing an explicit quantitative analysis based on singular
perturbations and nonlinear contraction theory. Complex systems are often
modular and hierarchic, and a central question is whether the whole system
behaves approximately as the "sum of its parts", or whether feedbacks between
modules modify qualitatively the modules behavior, and perhaps also generate
instabilities. We show that, when the individual nonlinear modules are
contracting (i.e., forget their initial conditions exponentially), a critical
separation of timescales exists between the dynamics of the modules and that of
the macro system, below which it behaves approximately as the stable sum of its
parts. Our analysis is fully nonlinear and provides explicit conditions and
error bounds, thus both quantifying and qualifying existing results on
near-decomposability. | Source: | arXiv, 1512.8464 | Services: | Forum | Review | PDF | Favorites |
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