Exponentially Long Transient Time to Synchronization of Coupled Chaotic Circle Maps in Dense Random Networks

We study the transition to synchronization in large, dense networks of chaotic circle maps, where an exact solution of the mean-field dynamics in the infinite network and all-to-all coupling limit is known. In dense networks of finite size and link probability of smaller than one, the incoherent sta...

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Published inEntropy (Basel, Switzerland) Vol. 25; no. 7; p. 983
Main Authors Mendonca, Hans Muller, Tönjes, Ralf, Pereira, Tiago
Format Journal Article
LanguageEnglish
Published Switzerland MDPI AG 27.06.2023
MDPI
Subjects
Analysis
chaotic maps
Coupling
Exact solutions
finite size effects
mean-field analysis
Networks
Oscillators
random networks
Synchronism
synchronization
Thermodynamics
Time synchronization
Germany
synchronization
finite size effects
chaotic maps
mean-field analysis
random networks
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Summary:We study the transition to synchronization in large, dense networks of chaotic circle maps, where an exact solution of the mean-field dynamics in the infinite network and all-to-all coupling limit is known. In dense networks of finite size and link probability of smaller than one, the incoherent state is meta-stable for coupling strengths that are larger than the mean-field critical coupling. We observe chaotic transients with exponentially distributed escape times and study the scaling behavior of the mean time to synchronization.
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These authors contributed equally to this work.
ISSN:1099-4300
1099-4300
DOI:10.3390/e25070983