Interaction network effects on position- and velocity-based models of collective motion

Area of Science:

• Physics
• Complex Systems
• Network Science

Background:

• Collective motion emerges from local interactions in systems of self-propelled agents.
• The structure of interaction networks (topology) can influence the emergent behavior and stability of these systems.
• Understanding this relationship is crucial for fields ranging from biology to robotics.

Purpose of the Study:

• To investigate how different interaction network topologies affect self-organized collective motion in two minimal agent-based models.
• To analyze the relationship between network structure and the resilience of ordered collective states to noise.
• To compare the effects of topology in the Vicsek model and the Active-Elastic (AE) model.

Main Methods:

• Simulations of the Vicsek model and the Active-Elastic (AE) model with varying network topologies.
• Topologies ranged from nearest-neighbor networks to random networks with homogeneous and power-law degree distributions.
• Analysis of the critical noise level required to disrupt the ordered collective state.

Main Results:

• In the Vicsek model, increased random connections (small-world effects) enhanced resilience to noise.
• Unexpectedly, in the AE model, increased random connections with power-law distributions reduced resilience to noise.
• This reduction in the AE model was attributed to localized low-energy modes facilitated by agents with few connections.

Conclusions:

• Interaction network topology has a profound impact on the self-organization and noise resilience of collective motion.
• The specific model dynamics (Vicsek vs. AE) determine how network structure influences collective behavior.
• Findings have implications for understanding biological swarms and improving decentralized control in swarm robotics.