Scalar model of flocking dynamics on complex social networks

Area of Science:

• Collective behavior
• Complex systems
• Social network analysis

Background:

• Flocking dynamics are crucial in collective motion across various species.
• Understanding social interactions' role in flocking is key to collective behavior research.
• Previous models like the Vicsek model provide a foundation for studying flocking.

Purpose of the Study:

• To investigate the impact of long-range social interactions on flocking dynamics.
• To analyze how network heterogeneity influences collective motion.
• To extend the analytical study of flocking behavior in complex social structures.

Main Methods:

• Development and analysis of a scalar model for collective motion.
• Embedding the model within a complex network representing social interactions.
• Analytical investigation using a modified scalar model and heterogeneous mean-field approximation.

Main Results:

• A phase transition between ordered and disordered phases was observed in networks with low heterogeneity.
• High levels of network heterogeneity were found to suppress the phase transition, maintaining an ordered state.
• Phenomenology analogous to the Vicsek model was identified.

Conclusions:

• Network structure significantly influences flocking dynamics and phase transitions.
• Heterogeneity in social interactions can lead to consistently ordered collective behavior.
• The study provides a framework for analytically studying flocking on complex social network topologies.