Discontinuous phase transition in the Kuramoto model with asymmetric dynamic interaction

Area of Science:

• Complex systems
• Nonlinear dynamics
• Statistical physics

Background:

• The Kuramoto model describes synchronization in coupled oscillator systems.
• A key characteristic is the difference between synchronized and average intrinsic frequencies.
• Asymmetric interactions may explain this frequency difference.

Purpose of the Study:

• Investigate critical behavior in a modified Kuramoto model with asymmetric dynamics.
• Understand how asymmetric interactions influence phase transitions.
• Compare findings with the conventional Kuramoto model.

Main Methods:

• Analysis of a modified Kuramoto model with asymmetric dynamic interaction.
• Examination of phase transition properties.
• Comparative study against the conventional Kuramoto model with phase reflection symmetry.

Main Results:

• A discontinuous phase transition emerges when oscillators interact only with those ahead.
• The modified model exhibits different transition behavior compared to the symmetric conventional model.
• Dynamical symmetry breaking and dynamic interaction structure changes are identified.

Conclusions:

• Asymmetric interactions fundamentally alter the nature of phase transitions in oscillator networks.
• Dynamical symmetry breaking is crucial for inducing discontinuous transitions.
• The modified Kuramoto model provides insights into frequency differences in synchronized systems.