Partial synchronization and partial amplitude death in mesoscale network motifs.

Area of Science:

• Complex systems
• Network science
• Nonlinear dynamics

Background:

• Oscillator networks exhibit complex spatio-temporal patterns.
• Understanding the relationship between network structure and emergent behavior is crucial.

Purpose of the Study:

• To introduce a concept for analytically predicting complex patterns in networks of Stuart-Landau oscillators.
• To link network topology directly to the emergence of partial amplitude death and synchronization.

Main Methods:

• Analysis of networks with linear symmetric and instantaneous coupling.
• Focus on network topology for pattern prediction.
• Investigation of Stuart-Landau oscillators.

Main Results:

• A concept is introduced to analytically predict complex space-time patterns based solely on network topology.
• Partial amplitude death and partial synchronization patterns are identified in various undirected networks (up to 5 nodes).
• The prediction concept is robust to frequency mismatch and extensible to larger networks.

Conclusions:

• Network topology is a key determinant of complex spatio-temporal patterns in oscillator networks.
• The stability of complete in-phase synchronization is directly related to specific topological eigenvalues.
• This work provides a powerful tool for understanding and predicting collective dynamics in complex networks.