Fate of vortex-synchronized state in oscillator networks with node defects

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Network Science

Background:

• Kuramoto oscillator networks are fundamental models for studying synchronization phenomena.
• Understanding network robustness against defects and noise is crucial for real-world applications.

Purpose of the Study:

• To investigate synchronization dynamics in a 2D Kuramoto oscillator network on a square lattice.
• To analyze the impact of local node defects and noise on the stability of synchronized states.

Main Methods:

• Simulating a Kuramoto oscillator network with a 2D square-lattice configuration.
• Utilizing random initial phases sampled from a von Mises distribution.
• Introducing temporal white noise and spatial noise (random oscillator frequencies).

Main Results:

• The network achieves a phase-locking vortex synchronized state in the long time limit.
• Vortex state stability is sensitive to local node defects, challenging conventional robustness assumptions.
• Spatial noise, above a threshold, can render the vortex state immune to local defects.

Conclusions:

• The vortex synchronized state in Kuramoto networks exhibits unexpected sensitivity to local defects.
• Spatial noise can play a protective role, enhancing the resilience of synchronized networks against perturbations.