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Updated: Sep 8, 2025

Sedimentation Equilibrium of a Small Oligomer-forming Membrane Protein: Effect of Histidine Protonation on Pentameric Stability
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Basin sizes depend on stable eigenvalues in the Kuramoto model.

Antonio Mihara1, Michael Zaks2, Elbert E N Macau3

  • 1Departamento de Física, Universidade Federal de São Paulo,UNIFESP, 09913-030, Campus Diadema, São Paulo, Brazil.

Physical Review. E
|June 16, 2022
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Summary
This summary is machine-generated.

Global statistics and basin sizes for the Kuramoto model can be estimated using eigenvalues of synchronized states. This local analysis unexpectedly reveals global dynamic properties of the coupled phase oscillator system.

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Area of Science:

  • Complex systems
  • Nonlinear dynamics
  • Statistical physics

Background:

  • The Kuramoto model describes synchronization in networks of coupled oscillators.
  • Understanding global dynamics from local properties is a significant challenge in nonlinear systems.

Purpose of the Study:

  • To demonstrate that global statistics and basin of attraction sizes in the Kuramoto model can be derived from local eigenvalue analysis.
  • To connect local equilibrium properties with global dynamic behaviors.

Main Methods:

  • Analytical estimation using eigenvalues of stable synchronized states.
  • Leveraging recent theoretical frameworks involving Koopman and Perron-Frobenius operators.
  • Validation through numerical simulations.

Main Results:

  • A method to estimate global properties of the Kuramoto model using eigenvalues of stable synchronized states.
  • Demonstration that local analysis can indeed predict global dynamic features.
  • Confirmation of analytical findings with established numerical simulations.

Conclusions:

  • Local eigenvalue analysis of stable synchronized states provides a powerful tool for understanding global dynamics in the Kuramoto model.
  • This approach offers an unexpected yet effective way to bridge local and global properties in nonlinear dynamical systems.