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Synchronization of fluctuating delay-coupled chaotic networks.

Manuel Jiménez-Martín1, Javier Rodríguez-Laguna1, Otti D'Huys2

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Physical Review. E
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Summary
This summary is machine-generated.

Random network switching can improve synchronization stability in chaotic systems with time-delayed interactions. Faster network fluctuations enhance stability, while slower ones diminish it, with notable effects in finite-size networks.

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Area of Science:

  • Complex systems
  • Network science
  • Chaos theory

Background:

  • Studying synchronization in complex networks is crucial for understanding emergent behaviors.
  • Time-delayed interactions and fluctuating network structures introduce significant challenges to synchronization.
  • Small-world networks offer unique properties for information propagation and synchronization.

Purpose of the Study:

  • To investigate the impact of fluctuating interactions on the synchronization of chaotic units.
  • To compare synchronization in static versus dynamic small-world networks under large time delays.
  • To identify conditions that enhance or disrupt synchronization stability.

Main Methods:

  • Analysis of Bernoulli and Logistic chaotic units within small-world networks.
  • Comparison of synchronization properties in static and randomly switching networks.
  • Exploration of synchronization across various fluctuation time scales relative to time delays.

Main Results:

  • Random network switching can enhance the stability of synchronized states.
  • Synchronization stability is maximized when network fluctuations are much faster than time delays.
  • Synchronization is lost for very slow fluctuations, with a resynchronizing effect observed in finite-size networks at specific fluctuation scales.
  • Characteristic oscillations, related to time-delay, are observed during transitions to and from synchronized states.

Conclusions:

  • Network dynamics, specifically random switching, play a critical role in the synchronization of chaotic systems.
  • The interplay between fluctuation speed and time delay determines synchronization stability.
  • Finite-size effects and network topology influence synchronization dynamics in non-trivial ways.