Analytical foundation for adversarial synchronization control in oscillator networks

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Network Science

Background:

• Kuramoto oscillator networks exhibit collective synchronization.
• Adversarial perturbations can influence synchronization dynamics.
• Previous studies observed significant amplification of synchronization via perturbations.

Purpose of the Study:

• To provide an analytical foundation for adversarial synchronization control in Kuramoto oscillator networks.
• To derive a closed-form expression for the effect of perturbations on the order parameter.
• To explain the mechanisms behind synchronization enhancement and suppression.

Main Methods:

• Ott-Antonsen reduction for analytical treatment.
• Derivation of closed-form expressions for perturbation effects.
• Fixed-point analysis for stability and asymmetry.
• Annealed network approximation for network generalization.

Main Results:

• Each adversarial perturbation (kick) yields a finite, coupling-independent increment in the order parameter.
• The theory explains amplification through weak synchronization, slow relaxation, and mean-field feedback.
• A fundamental asymmetry exists between enhancement and suppression, with suppression linked to noise-induced escape.
• The framework accurately models synchronization in scale-free networks, revealing a decoupling of kick sensitivity and mean-field dominance.

Conclusions:

• The study establishes a tractable theoretical basis for understanding and designing adversarial synchronization control.
• The findings offer insights into manipulating collective behavior in oscillator networks.
• The developed framework is applicable to various network structures and perturbation strategies.