Repulsive synchronization in complex networks

Area of Science:

• Complex Networks
• Nonlinear Dynamics
• Statistical Physics

Background:

• Synchronization is a key phenomenon in complex autonomous systems, where coupled oscillators achieve phase-locking.
• The Kuramoto model is a standard framework for studying synchronization transitions in networks.
• Phase shifts in oscillator coupling can significantly alter synchronization dynamics.

Purpose of the Study:

• To investigate the influence of a tunable phase-lag parameter (α) on synchronization transitions in the Kuramoto model.
• To identify and characterize novel synchronization patterns induced by phase shifts, particularly repulsive coupling.

Main Methods:

• Simulations of the Kuramoto model with a tunable phase-lag parameter α.
• Analysis of synchronization transitions under varying coupling strengths and phase-lag values.
• Introduction of the frequency dispersion parameter to detect synchronization, especially for patterns not captured by the standard order parameter r.

Main Results:

• Phase frustration, introduced by the phase-lag parameter, can lead to desynchronization.
• Two global synchronization regions were identified for α∈[0,2π) under sufficiently large coupling.
• A rare synchronization pattern, termed 'repulsive synchronization,' was detected near α=π, induced by repulsive coupling.

Conclusions:

• Phase shifts, particularly repulsive coupling, can induce unique synchronization behaviors like 'repulsive synchronization'.
• The standard order parameter (r) is insufficient to describe repulsive synchronization, necessitating the use of frequency dispersion.
• Understanding these phase-lag-induced dynamics is crucial for characterizing synchronization in diverse complex networks.