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Criticality in conserved dynamical systems: experimental observation vs. exact properties.
Dimitrije Marković1, Claudius Gros, André Schuelein
1Institute for Theoretical Physics, Johann Wolfgang Goethe University, Frankfurt am Main, Germany.
Chaos (Woodbury, N.Y.)
|April 6, 2013
Summary
Critical dynamical systems, like routing models, exhibit conserved information flow governed by cyclic attractors. While not inherently scale-invariant, they display power-law scaling when stochastically sampled, highlighting the importance of observation methods.
Area of Science:
- Complex Systems
- Statistical Physics
- Network Science
Background:
- Conserved dynamical systems are often characterized as critical.
- Criticality in systems implies unique scaling properties and emergent behaviors.
- Understanding information flow in such systems is key to their analysis.
Purpose of the Study:
- To rigorously analyze a class of critical routing models equivalent to random maps.
- To investigate information flow dynamics governed by cyclic attractors.
- To differentiate intrinsic system properties from observed behavior under stochastic sampling.
Main Methods:
- Solving routing models in the thermodynamic limit.
- Analyzing cycle length distributions for complete graphs.
- Calculating weighted average attractor lengths under stochastic phase space sampling.
Main Results:
- Logarithmic corrections to power-law scaling were found for mean cycle length.
- Sub-polynomial growth was observed for the total number of cycles.
- Power-law scaling emerged for weighted average attractor lengths in vertex routing models.
Conclusions:
- Critical dynamical systems are not generically scale-invariant.
- Stochastic sampling can induce apparent power-law scaling.
- Distinguishing intrinsic properties from observed behavior is crucial for accurate interpretation.
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