Effective Subnetwork Topology for Synchronizing Interconnected Networks of Coupled Phase Oscillators

Area of Science:

• Complex systems
• Network science
• Computational neuroscience

Background:

• Real-world systems, such as the brain, are often structured as networks of networks (NoNs).
• Understanding how network topology influences collective behavior, like synchrony, is crucial for these systems.

Purpose of the Study:

• To investigate the impact of subnetwork topology on the global synchrony of heterogeneous phase oscillator networks.
• To determine how different coupling strategies affect synchronization in NoNs.

Main Methods:

• Utilized the Kuramoto order parameter to quantify the degree of synchrony.
• Evaluated synchrony by measuring the minimum coupling strength required to exceed a threshold for the order parameter.
• Modeled NoNs with heterogeneous phase oscillators and varying subnetwork degree distributions.

Main Results:

• Heterogeneous subnetwork degree distributions in NoNs promote synchrony with weaker interconnections compared to isolated networks.
• High-degree nodes play a significant role in achieving global synchrony.
• Directly coupling subnetworks with the largest variation in average natural frequencies is effective for synchronizing the entire system.

Conclusions:

• Subnetwork topology is a critical factor in determining the coordinated dynamics of NoNs.
• The findings offer insights into the topological basis of synchrony in complex systems, including biological networks like the brain.
• Optimizing interconnections based on subnetwork topology can enhance global synchrony.