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Explosive synchronization transitions in complex neural networks.

Hanshuang Chen1, Gang He, Feng Huang

  • 1School of Physics and Materials Science, Anhui University, Hefei 230039, People's Republic of China.

Chaos (Woodbury, N.Y.)
|October 5, 2013
PubMed
Summary
This summary is machine-generated.

Explosive synchronization transitions were observed in Barabási-Albert networks when oscillator frequencies correlated with node degrees. This explosive synchronization was not found in Erdös-Rényi networks, and degree assortativity hindered it.

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Area of Science:

  • Complex systems
  • Nonlinear dynamics
  • Network science

Background:

  • Explosive synchronization transitions have been reported in phase and chaotic oscillator networks.
  • Coupled oscillators exhibit complex synchronization behaviors depending on network topology and dynamics.

Purpose of the Study:

  • Investigate the effect of microscopic correlations between dynamics and topology on phase synchronization transitions.
  • Examine these effects in Barabási-Albert (BA) scale-free networks and Erdös-Rényi (ER) random networks using coupled FitzHugh-Nagumo oscillators.

Main Methods:

  • Simulated coupled FitzHugh-Nagumo oscillators on BA and ER networks.
  • Varied the correlation between natural frequencies and node degrees.
  • Analyzed the synchronization transition by observing hysteresis loops in the synchronization diagram.

Main Results:

  • A strong hysteresis loop, indicating explosive synchronization, emerged in BA networks when natural frequencies positively correlated with node degrees and frequency distribution width exceeded a threshold.
  • In contrast, ER networks exhibited continuous synchronization transitions regardless of frequency distribution width.
  • Degree assortativity was found to be unfavorable for explosive synchronization.

Conclusions:

  • Microscopic correlations between oscillator dynamics and network topology can induce explosive synchronization transitions in scale-free networks.
  • Network homogeneity (ER networks) and degree assortativity suppress explosive synchronization.
  • The findings highlight the crucial role of network structure and dynamical properties in determining synchronization behavior.