Dynamics in the Sakaguchi-Kuramoto model with two subpopulations [corrected]

Area of Science:

• Complex systems
• Nonlinear dynamics
• Theoretical physics

Background:

• The Sakaguchi-Kuramoto model describes coupled oscillators.
• Understanding synchronization dynamics is crucial in various scientific fields.
• Investigating variants with multiple subpopulations reveals complex behaviors.

Purpose of the Study:

• To analyze the dynamics of a modified Sakaguchi-Kuramoto phase oscillator model.
• To investigate the interplay between two subpopulations with distinct parameters.
• To identify and characterize different emergent states, including stationary and traveling waves.

Main Methods:

• Utilizing the Ott-Antonson ansatz for analytical insights.
• Employing numerical simulations to explore model dynamics.
• Analyzing parameter spaces to understand state transitions.

Main Results:

• Identified stationary synchronous states, specifically generalized pi states.
• Observed two distinct types of traveling wave states.
• Demonstrated that traveling wave states represent the dominant dynamics.
• Found a smooth transition pathway between stationary and traveling wave states.

Conclusions:

• The studied Sakaguchi-Kuramoto variant exhibits rich dynamics beyond simple synchronization.
• Traveling waves are a prevalent emergent behavior in this two-subpopulation system.
• Parameter control allows for continuous transitions between different dynamic regimes.