Phase synchronization and polarization ordering of globally coupled oscillators

Area of Science:

• Complex systems
• Nonlinear dynamics
• Statistical physics

Background:

• Globally coupled oscillators are fundamental in various scientific fields.
• Understanding collective behaviors like synchronization and ordering is crucial.

Purpose of the Study:

• To introduce a prototype model for globally coupled oscillators with random frequencies and polarization.
• To investigate the collective transitions observed in this model.
• To develop a theoretical framework for analyzing synchronization and ordering phenomena.

Main Methods:

• Development of a prototype model for globally coupled oscillators.
• Introduction of global-phase and polarization order parameters.
• Numerical simulations to observe collective transitions.
• Development of a self-consistent theory for order parameter analysis.

Main Results:

• Identified two distinct collective transitions: phase synchronization and polarization ordering.
• Established that phase synchronization is a prerequisite for polarization order enhancement.
• Determined the critical coupling value for the onset of global-phase synchrony.
• Validated theoretical predictions against numerical results.

Conclusions:

• The model exhibits predictable collective transitions governed by coupling strength.
• Phase synchronization is a necessary condition for polarization ordering in this system.
• The developed self-consistent theory accurately describes the emergent order parameters.