Cluster formation due to repulsive spanning trees in attractively coupled networks

Area of Science:

• Complex Systems
• Network Science
• Nonlinear Dynamics

Background:

• Coupled nonlinear oscillators are crucial for understanding collective behaviors.
• Cluster synchronization is vital in technological and biological systems.
• Existing research primarily focuses on attractive coupling, neglecting competing interactions.

Purpose of the Study:

• Investigate the impact of repulsive spanning trees on cluster formation in attractively coupled oscillator networks.
• Predict cluster membership and network frustration irrespective of local oscillator dynamics.
• Analyze the stability of emergent cluster states.

Main Methods:

• Utilizing a master stability function approach.
• Analyzing networks of limit-cycle oscillators with both attractive and repulsive coupling.
• Employing mathematical modeling to predict cluster formation and stability.

Main Results:

• Successfully predicted node membership in emergent clusters.
• Demonstrated the emergence of network frustration.
• Validated the formation of solitary states and antisynchronization for specific network structures.
• Determined the local asymptotic stability of cluster states.

Conclusions:

• Repulsive interactions significantly impact cluster formation in coupled oscillator networks.
• The findings are independent of specific local dynamics, highlighting general network principles.
• This work provides a framework for understanding complex collective behaviors in systems with competing interactions.