Frustration tuning and perfect phase synchronization in the Kuramoto-Sakaguchi model

Area of Science:

• Complex systems
• Network dynamics
• Nonlinear dynamics

Background:

• The Kuramoto model describes synchronization in coupled oscillator systems.
• Frustration in these models, particularly the Kuramoto-Sakaguchi model, impacts synchronization dynamics on networks.
• Understanding conditions to enhance synchronization in frustrated networks is crucial for various applications.

Purpose of the Study:

• To analyze conditions for enhancing synchronization in frustrated Kuramoto-Sakaguchi models on sparse networks.
• To develop a tuning scheme for frustration parameters to control synchronization.
• To investigate a codynamics approach for dynamic frustration parameter tuning.

Main Methods:

• Numerical optimization techniques
• Linear stability analysis
• Dimensional reduction analysis
• Finite-size scaling analysis

Main Results:

• A simple tuning scheme for node-specific frustration parameters was developed, dependent on native frequencies and degrees.
• Partial application of the tuning rule significantly reduces the critical coupling for synchronization onset.
• A codynamics approach allows simultaneous dynamic tuning of frustration parameters.
• Codynamics enhance synchronization on slow time scales but impede it on fast time scales.

Conclusions:

• The developed tuning scheme effectively enhances synchronization in frustrated Kuramoto-Sakaguchi models.
• Dynamic tuning via codynamics offers a flexible method to control synchronization, with time scale dependency.
• These findings provide insights into controlling collective behavior in complex networks.