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Explosive synchronization with asymmetric frequency distribution.

Wenchang Zhou1, Lumin Chen1,2, Hongjie Bi1

  • 1Department of Physics, East China Normal University, Shanghai, 200241, China.

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|August 15, 2015
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Summary
This summary is machine-generated.

This study explores synchronization in a generalized Kuramoto model with asymmetric oscillator frequencies. We found that the synchronization transition order changes with frequency shifts, revealing new coherent states.

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Area of Science:

  • Complex systems
  • Nonlinear dynamics
  • Statistical physics

Background:

  • The Kuramoto model is a fundamental framework for studying synchronization in coupled oscillator systems.
  • Asymmetric frequency distributions in oscillators can lead to complex synchronization behaviors not observed in symmetric cases.

Purpose of the Study:

  • To investigate synchronization phenomena in a generalized Kuramoto model with frequency-weighted coupling and asymmetric oscillator frequency distributions.
  • To analyze the impact of asymmetric frequency distributions on the order of synchronization transitions.
  • To identify and characterize novel coherent states in such systems.

Main Methods:

  • Utilized a generalized Kuramoto model with frequency-weighted coupling.
  • Analyzed systems with various unimodal asymmetric frequency distributions (Lorentzian, Gaussian, triangle, Rayleigh).
  • Performed theoretical analysis to understand the relationship between frequency asymmetry and synchronization type.

Main Results:

  • Synchronization transition order shifts from first to second order as the central frequency shifts positively.
  • Identified two distinct coherent states: one with two phase-locking clusters at the same frequency, and another with clusters at different frequencies.
  • Observed that high-frequency oscillators form clusters while low-frequency oscillators remain unentrained in one state.

Conclusions:

  • Asymmetric frequency distributions significantly influence the type of synchronization transition in the Kuramoto model.
  • The identified coherent states provide new insights into the complex dynamics of coupled oscillator systems with non-uniform frequencies.
  • Theoretical analysis supports the observed phenomena, linking frequency asymmetry to synchronization behavior and coherent state formation.