Phase slips in coupled oscillator systems

Area of Science:

• Nonlinear Dynamics
• Complex Systems
• Network Science

Background:

• Phase slips are key events in coupled oscillator systems, marking transitions to phase synchrony.
• Previous analyses often relied on identifying saddle-node remnants or 'ghosts' for phase slip characterization.

Purpose of the Study:

• To provide a more precise, quantitative description of phase slip dynamics in coupled oscillator systems.
• To investigate the underlying mechanisms of phase shifts and phase sticks.

Main Methods:

• Detailed examination of the dynamics in sets of phase oscillators.
• Analysis of phase velocities and their stationary points.
• Study of various systems exhibiting phase synchrony, including those with and without saddle-node ghosts, similarity-dependent coupling, and coupled chaotic oscillators.

Main Results:

• Phase shifts and phase sticks occur at stationary points of phase velocities.
• In networks of coupled phase oscillators, individual phase slips typically do not happen simultaneously.
• Demonstrated phase synchrony in diverse systems, including those lacking traditional saddle-node ghosts.

Conclusions:

• The study offers a refined, quantitative understanding of phase slip phenomena in coupled oscillators.
• Identified stationary points of phase velocities as critical for phase slip events.
• Extended the analysis to diverse oscillator network configurations, highlighting the complexity of synchrony.