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Dynamical phase transitions in graph cellular automata
Freya Behrens1, Barbora Hudcová2,3, Lenka Zdeborová1
1Statistical Physics Of Computation Laboratory, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland.
Graph cellular automata on random graphs allow for analytical insights into complex system dynamics. This research introduces "conforming nonconformist" rules, revealing phase transitions in opinion formation models.
Area of Science:
- Complex Systems
- Statistical Physics
- Network Science
Background:
- Discrete dynamical systems, like cellular automata, display complex global behavior from simple local rules.
- Analyzing global dynamics of traditional cellular automata is often analytically challenging due to their regular grid structure.
Purpose of the Study:
- To introduce and analyze graph cellular automata (GCA) on random graphs as a more tractable model.
- To investigate the global dynamics of GCA, particularly those with
- conforming nonconformist
- update rules, using analytical methods.
Main Methods:
- Development and application of the dynamical cavity method and its backtracking variant.
- Analysis of GCA on sparse random graphs to derive asymptotically exact results.
- Modeling opinion formation dynamics using GCA with specific update rules.
Main Results:
- The dynamical cavity method provides analytical tractability for GCA on random graphs.
- Identified sharp dynamical phase transitions in GCA with
- conforming nonconformist
- rules.
- Characterized transitions in terms of convergence speed and attractor types, relating to consensus and opinion coexistence.
Conclusions:
- Relaxing the grid structure to a random graph significantly enhances analytical understanding of cellular automata dynamics.
- The
- conforming nonconformist
- GCA model offers a novel framework for studying opinion formation and predicting consensus emergence.
- The findings provide insights into the conditions governing consensus formation versus persistent coexistence of opinions in social or information networks.
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