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Xiyun Zhang1, Yong Zou1, S Boccaletti2

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This study introduces a suppressive rule for explosive synchronization (ES), unifying it with explosive percolation (EP). This rule explains the abrupt formation of giant synchronized clusters in complex networks, akin to the Achlioptas process.

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Area of Science:

  • Complex networks
  • Statistical physics
  • Dynamical systems

Background:

  • Explosive synchronization (ES) and explosive percolation (EP) are distinct phenomena in complex networks.
  • EP's mechanism involves the Achlioptas process and a suppressive rule for giant component formation.
  • ES occurs in dynamical phase space, while EP occurs in configuration space.

Purpose of the Study:

  • Introduce an equivalent suppressive rule for explosive synchronization.
  • Unify the frameworks of explosive synchronization and explosive percolation.
  • Investigate the transition of ES from explosive to second-order phase transition.

Main Methods:

  • Introduction of a novel suppressive rule for explosive synchronization.
  • Analysis of cluster formation dynamics under the suppressive rule.
  • Examination of the impact of breaking the suppressive rule on ES behavior.

Main Results:

  • The suppressive rule leads to multiple small synchronized clusters before the critical point.
  • An abrupt formation of a giant synchronized cluster occurs at the critical coupling strength.
  • Breaking the suppressive rule causes explosive synchronization to degrade into a second-order phase transition.

Conclusions:

  • The introduced suppressive rule is a dynamical counterpart to the Achlioptas process.
  • Explosive synchronization and explosive percolation can be unified within a single theoretical framework.
  • The findings offer new insights into the behavior of complex networks and phase transitions.