Phase coherence induced by correlated disorder.

Area of Science:

• Complex systems
• Statistical physics
• Nonlinear dynamics

Background:

• Coupled phase oscillators are fundamental models for synchronization phenomena.
• Quenched disorder in coupling strengths and natural frequencies typically inhibits phase coherence.
• Previous studies showed absence of synchronization with uncorrelated disorder.

Purpose of the Study:

• To investigate the impact of correlated disorder on synchronization in coupled phase oscillators.
• To explore how correlating disorder with natural frequencies affects system coherence.
• To determine conditions under which phase coherence can emerge in disordered oscillator networks.

Main Methods:

• Utilized a mean-field model of coupled phase oscillators.
• Introduced quenched disorder in both coupling strengths and natural frequencies.
• Correlated the sign of interaction with the natural frequency of each oscillator.
• Analyzed system behavior for symmetrically and asymmetrically correlated disorder.

Main Results:

• Symmetrically correlated disorder with zero mean leads to spontaneous synchronization below a critical frequency distribution width.
• Asymmetrically correlated disorder results in coherent traveling waves with a non-zero, rotating complex order parameter.
• Correlated disorder, in both symmetric and asymmetric cases, was shown to trigger phase coherence.

Conclusions:

• Correlated disorder is a key factor in enabling phase coherence in systems of coupled oscillators.
• The nature of the correlation (symmetric vs. asymmetric) dictates the emergent dynamics, such as synchronization or traveling waves.
• This work highlights a mechanism for achieving order in complex, disordered systems.