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Explosive synchronization coexists with classical synchronization in the Kuramoto model.

Michael M Danziger1, Olga I Moskalenko2, Semen A Kurkin2

  • 1Department of Physics, Bar-Ilan University, Ramat Gan, Israel.

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|July 3, 2016
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Summary
This summary is machine-generated.

Explosive synchronization in Kuramoto oscillators is more common than previously thought. This study reveals that explosive and standard synchronization phases coexist, even with partial coupling, suggesting natural occurrence in many systems.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Network Science

Background:

  • Recent studies reported explosive synchronization in adaptively coupled Kuramoto oscillators.
  • This phenomenon was previously thought to require specific conditions on node frequencies or network degree.
  • The coexistence of explosive and standard synchronization phases was not fully understood.

Purpose of the Study:

  • To investigate the coexistence of explosive and standard synchronization in adaptively coupled Kuramoto oscillator systems.
  • To extend mean-field theory to analyze partial coupling in these oscillator networks.
  • To determine the conditions under which explosive synchronization occurs in more general network configurations.

Main Methods:

  • Extension of mean-field theory for adaptively coupled oscillators to include partial coupling (fraction f).
  • Theoretical analysis to identify the existence of a metastable region for finite f > 0.
  • Large-scale GPU-accelerated simulations on networks with up to 10^6 nodes (N ~ 10^6).

Main Results:

  • A metastable region for explosive synchronization exists for all finite values of partial coupling (f > 0).
  • Explosive synchronization with hysteresis was observed in simulations for all finite couplings.
  • Explosive transitions were shown to coexist with standard transitions as partial coupling approaches zero (f → 0).

Conclusions:

  • Explosive synchronization is not limited to specific conditions and is expected in any adaptively coupled Kuramoto model with perturbations.
  • The phenomenon is far more likely to occur naturally in real-world systems than previously believed.
  • Partial coupling does not prevent explosive synchronization; instead, it broadens the conditions for its occurrence.