Robustness and fragility in coupled oscillator networks under targeted attacks

Area of Science:

• Complex systems
• Network science
• Nonlinear dynamics

Background:

• Coupled oscillator networks are fundamental to many natural and engineered systems.
• Network robustness against node failures is crucial for system reliability.
• Existing measures of robustness are limited, particularly for targeted attacks.

Purpose of the Study:

• To derive a general analytical formula for the critical fraction of failed nodes in coupled oscillator networks.
• To extend the understanding of network robustness beyond random failures to include targeted attacks.
• To identify key factors influencing the robustness and fragility of oscillator networks.

Main Methods:

• Analytical derivation of the critical fraction for network failure.
• Consideration of targeted attacks based on node degrees.
• Extension of the theory to networks with heterogeneous edge weights and nonidentical oscillators.
• Validation of analytical results through numerical experiments.

Main Results:

• A general formula for the critical fraction of node failures was derived.
• The formula applies to both random failures and targeted attacks.
• Network robustness is shown to depend on oscillator properties and network topology.
• Key factors determining network fragility were identified.

Conclusions:

• The derived formula provides a unified measure of network robustness against various failure scenarios.
• Understanding the impact of targeted attacks is essential for designing resilient complex systems.
• This work offers insights into the fundamental principles governing the stability of coupled oscillator networks.