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Explosive synchronization is discontinuous.

Vladimir Vlasov1, Yong Zou2, Tiago Pereira3,4

  • 1Institute of Physics, Potsdam University, 14469 Potsdam, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 15, 2015
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Summary
This summary is machine-generated.

Spontaneous explosive transitions to collective behavior in heterogeneous networks are discontinuous. This study confirms this discontinuous transition in star graphs, explaining the hysteresis behavior through network parameters.

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Area of Science:

  • Complex systems
  • Network science
  • Statistical physics

Background:

  • Spontaneous explosive transitions represent abrupt shifts to collective behavior in heterogeneous networks.
  • These transitions occur when node frequencies correlate positively with node degree.
  • Previous conjectures suggested these transitions are discontinuous, supported by numerical hysteresis observations.

Purpose of the Study:

  • To analyze the nature of explosive synchronization in star graphs.
  • To confirm the discontinuous nature of the transition to and from collective behavior.
  • To elucidate the hysteresis behavior in relation to graph parameters.

Main Methods:

  • Analysis of explosive synchronization dynamics.
  • Investigation in the context of star graphs.
  • Examination of the thermodynamic limit and finite-size graph behavior.

Main Results:

  • The transition to and from collective behavior in star graphs is confirmed to be discontinuous in the thermodynamic limit.
  • The discontinuous transition is linked to the nonlinear behavior of the order parameter, exhibiting multiple fixed points.
  • Hysteresis behavior is successfully explained in terms of graph parameters.

Conclusions:

  • The study confirms the discontinuous nature of explosive synchronization transitions in star graphs.
  • The findings provide a theoretical explanation for hysteresis in these systems.
  • The developed predictions accurately describe the behavior of finite-size graphs.