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Updated: Mar 15, 2026

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Synchronization in the random-field Kuramoto model on complex networks.

M A Lopes1,2,3,4, E M Lopes1, S Yoon1

  • 1Department of Physics & I3N, University of Aveiro, 3810-193 Aveiro, Portugal.

Physical Review. E
|August 31, 2016
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Summary
This summary is machine-generated.

Random pinning fields influence synchrony in the Kuramoto model. A tricritical point emerges, altering phase transitions in complete and scale-free networks, with second-order transitions persisting even under strong fields.

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Area of Science:

  • Complex Systems
  • Statistical Physics
  • Network Science

Background:

  • The Kuramoto model describes synchronization in coupled oscillator systems.
  • Understanding the impact of external fields on network synchrony is crucial.
  • Complex networks exhibit diverse structures influencing emergent behaviors.

Purpose of the Study:

  • To investigate the effect of random pinning fields on synchronization in the Kuramoto model.
  • To analyze phase transitions in complete and scale-free networks under varying field conditions.
  • To determine the critical behavior of the order parameter with different field magnitude distributions.

Main Methods:

  • Application of the Ott-Antonsen method for analytical solutions.
  • Utilizing the annealed-network approximation for critical behavior analysis.
  • Numerical simulations to validate analytical findings.

Main Results:

  • A tricritical point is identified, transitioning second-order to first-order phase transitions for specific network types (complete, scale-free with γ>5).
  • Scale-free networks with 2<γ≤5 exhibit second-order transitions, except for γ=3 where it's infinite order.
  • Gaussian random fields do not suppress second-order transitions, though they increase critical coupling for γ>3.

Conclusions:

  • Random pinning fields significantly alter synchronization dynamics and phase transitions in the Kuramoto model.
  • Network topology plays a critical role in how external fields affect synchrony.
  • The findings offer insights into collective behavior in complex systems under external perturbations.