Exponentially Long Transient Time to Synchronization of Coupled Chaotic Circle Maps in Dense Random Networks
Hans Muller Mendonca1, Ralf Tönjes2, Tiago Pereira1
1Instituto de Ciências Matemáticas e Computação, Universidade de São Paulo, São Carlos 13566-590, SP, Brazil.
Entropy (Basel, Switzerland)
|July 29, 2023
Summary
In large networks of chaotic maps, synchronization is delayed in finite networks. The study reveals meta-stable states and chaotic transients impacting the time to synchronization.
Area of Science:
- Complex systems
- Network dynamics
- Chaos theory
Background:
- Synchronization is a fundamental phenomenon in coupled dynamical systems.
- Mean-field theory provides exact solutions for infinite, all-to-all coupled networks.
- Finite-size effects and sparse connectivity can alter synchronization transitions.
Purpose of the Study:
- Investigate the transition to synchronization in large, dense networks of chaotic circle maps.
- Analyze deviations from mean-field predictions in finite networks.
- Characterize the dynamics of the incoherent state and the approach to synchronization.
Main Methods:
- Utilized chaotic circle maps as a model system.
- Simulated dense networks with finite size and varying link probabilities.
- Analyzed the stability of the incoherent state and escape times.
Main Results:
- The incoherent state is meta-stable for coupling strengths exceeding the mean-field critical value in finite networks.
- Observed chaotic transients with exponentially distributed escape times.
- Investigated the scaling behavior of the mean time to synchronization.
Conclusions:
- Finite network size and reduced connectivity lead to meta-stability and delayed synchronization.
- Chaotic transients are a significant feature of the synchronization transition in these systems.
- Understanding these deviations is crucial for predicting synchronization in realistic complex networks.
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