Heterogeneity enhances dynamic survivability of coupled oscillators

Area of Science:

• Complex Systems
• Network Science
• Nonlinear Dynamics

Background:

• Survivability is crucial for network security and functional integrity.
• Coupled oscillator systems are fundamental in various scientific and engineering domains.
• Understanding system resilience under external perturbations is a key challenge.

Purpose of the Study:

• Introduce and define dynamic survivability for coupled oscillator systems.
• Develop a general analytical framework and quantitative metrics to assess dynamic survivability.
• Investigate the impact of parameter heterogeneity on survivability against attacks.

Main Methods:

• Theoretical analysis of heterogeneous coupled oscillators under different network structures (all-to-all, complex networks).
• Derivation of closed-form expressions for critical attack cost.
• Numerical simulations to validate theoretical predictions and framework.

Main Results:

• Established a novel analytical framework for dynamic survivability in oscillator networks.
• Derived critical attack cost expressions for synchronization tasks.
• Demonstrated that increased parameter heterogeneity significantly enhances system survivability.

Conclusions:

• Parameter diversity, not homogeneity, is key to designing robust oscillator networks.
• The findings are general across various network topologies (random, scale-free).
• This work provides a new perspective on engineering resilient complex systems.