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Constrained growth of complex scale-independent systems
Laurent Hébert-Dufresne1,2, Antoine Allard1,3, Jean-Gabriel Young1
1Département de Physique, de Génie Physique, et d'Optique, Université Laval, Québec (Québec), Canada G1V 0A6.
Physical Review. E
|April 15, 2016
Summary
Complex systems often exhibit scale independence. This study proposes a minimal model combining preferential attachment and delayed temporal scaling to explain this emergent behavior across diverse fields.
Area of Science:
- Complex Systems Science
- Network Theory
- Dynamical Systems
Background:
- Scale independence is a common characteristic of complex systems, observed in fields like biology, economics, and sociology.
- Previous research has focused on the prevalence of scale independence, but less on the precise mechanisms driving its emergence.
- Idealized models often simplify system dynamics, potentially overlooking key factors contributing to scale-invariant distributions.
Purpose of the Study:
- To elucidate the minimal dynamical features required for the emergence of scale independence in complex systems.
- To contrast emergent scale independence with idealized models that assume its presence.
- To propose and validate a model that explains the growth toward scale independence.
Main Methods:
- Development of a minimal dynamical model incorporating preferential attachment and delayed temporal scaling.
- Analysis of the interplay between population growth and individual activity through temporal scaling delays.
- Empirical validation across diverse datasets, including scientific productivity, artistic output, sexual networks, and online traffic.
Main Results:
- A minimal model for scale independence requires preferential attachment and delayed temporal scaling.
- Delayed temporal scaling enhances the speed of convergence to scale independence.
- The model successfully predicts system evolution, enabling reconstruction of past states and future trajectories from snapshots.
- The model's applicability was confirmed across a wide range of human activities.
Conclusions:
- Preferential attachment and delayed temporal scaling are key drivers of scale independence in complex systems.
- The proposed model provides a precise evolutionary path toward scale independence.
- This framework offers a powerful tool for understanding and predicting the behavior of diverse complex systems.
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