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Partial locking in phase-oscillator populations with heterogenous coupling.

Can Xu1, Yonggang Wu2, Zhigang Zheng1

  • 1Institute of Systems Science and College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China.

Chaos (Woodbury, N.Y.)
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Summary
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We identified a criterion for partial locking in coupled phase oscillators, where synchronized and unsynchronized elements coexist. This finding advances understanding of synchronization phenomena in complex networks.

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Area of Science:

  • Physics
  • Complex Systems
  • Network Science

Background:

  • Coupled phase oscillators are fundamental models for synchronization phenomena.
  • Understanding partial locking is crucial for analyzing complex networked systems.

Purpose of the Study:

  • To establish a generic criterion for the onset of partial locking in a mean-field model of coupled phase oscillators.
  • To investigate the influence of quenched disorder and coupling heterogeneity on synchronization patterns.

Main Methods:

  • Analysis of a mean-field model with uniform natural frequencies.
  • Establishing correlations between disorder, coupling strength, and heterogeneities.
  • Analytical derivation of critical points for stationary state instability.
  • Utilizing a frequency-dependent Ott-Antonsen reduction and self-consistent approach.

Main Results:

  • A generic criterion for partial locking, characterized by coexisting phase-locked oscillators and drifters, was revealed.
  • Critical points for the instability of stationary states were determined analytically.
  • The bifurcation mechanism of equilibrium states was uncovered.
  • Coupling heterogeneity and correlation exponent were shown to influence emergent partial locking patterns.

Conclusions:

  • The study provides a fundamental criterion for partial locking in oscillator networks.
  • Findings offer insights into phase transitions and synchronization control in networked systems.
  • The research has potential applications in understanding and managing collective phenomena.