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Phase separation in coupled chaotic maps on fractal networks
K Tucci1, M G Cosenza, O Alvarez-Llamoza
1SUMA-CESIMO, Universidad de Los Andes, Mérida, Venezuela.
Summary
Coupled chaotic maps on fractal networks exhibit frozen phases, unlike regular lattices. This study analyzes phase ordering dynamics using persistence probability, revealing unique behaviors due to fractal geometry.
Area of Science:
- Complex Systems
- Statistical Physics
- Network Science
Background:
- Phase ordering dynamics are crucial for understanding complex systems.
- Previous studies on regular lattices show distinct phase transition behaviors.
- Fractal networks introduce unique structural properties influencing system dynamics.
Purpose of the Study:
- To investigate the phase ordering dynamics of coupled chaotic maps on fractal networks.
- To characterize the statistical properties using persistence probability.
- To contrast the behavior on fractal networks with that on Euclidean lattices.
Main Methods:
- Coupled chaotic maps were used to model the system.
- Persistence probability of equivalent spin variables was employed for statistical characterization.
- Analysis focused on the influence of fractal network structure on phase ordering.
Main Results:
- Persistence saturates and phase domains freeze for all coupling parameters on fractal networks.
- This behavior contrasts with the phase transition observed in regular Euclidean lattices.
- Discontinuities in the persistence curve are linked to stability changes of local phase configurations.
Conclusions:
- The fractal structure of networks fundamentally alters phase ordering dynamics.
- Phase freezing, rather than phase transitions, characterizes these systems.
- Understanding local configuration stability is key to explaining observed phenomena on fractals.