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Dynamics of critical Kauffman networks under asynchronous stochastic update
Florian Greil1, Barbara Drossel
1Institut für Festkörperphysik, Technische Universität Darmstadt, Germany.
Physical Review Letters
|August 11, 2005
Summary
In critical Boolean networks, asynchronous updates lead to a power-law increase in attractors. Attractor size grows exponentially with system size, unlike synchronous networks.
Area of Science:
- Complex systems
- Theoretical computer science
- Network dynamics
Background:
- Boolean networks are models for gene regulatory networks and other complex systems.
- Understanding the dynamics of these networks, particularly their attractors, is crucial for predicting system behavior.
- Previous studies often focused on synchronous updates, yielding different results.
Purpose of the Study:
- To investigate the behavior of attractors in critical Boolean networks under asynchronous stochastic updates.
- To compare these dynamics with those observed under synchronous updates.
- To characterize the scaling of attractor number and size with system size.
Main Methods:
- Analysis of critical Boolean networks with asynchronous stochastic updates.
- Mathematical modeling to derive scaling laws for attractor properties.
- Comparison of results with theoretical predictions for synchronous updates.
Main Results:
- The mean number of attractors grows as a power law with system size under asynchronous updates.
- The mean size of attractors increases as a stretched exponential with system size.
- This contrasts sharply with synchronous updates, where attractor number grows faster than any power law.
Conclusions:
- Asynchronous updates in critical Boolean networks lead to distinct scaling behaviors for attractors compared to synchronous updates.
- The power-law and stretched exponential scaling provide insights into the stability and complexity of these networks.
- These findings have implications for understanding biological systems and designing robust computational networks.
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