Unstable modes and bistability in delay-coupled swarms.

Area of Science:

• Robotics
• Complex Systems
• Control Theory

Background:

• Time delays in mobile-agent swarm networks are known to induce coherent rotational patterns.
• These spatiotemporal rotations can exhibit bistability with other swarm behaviors like milling and flocking.
• Existing bifurcation analyses often use inaccurate mean-field techniques, limiting predictive and control applications.

Purpose of the Study:

• To perform an exact stability analysis of swarming patterns in delay-coupled systems.
• To overcome limitations of mean-field techniques in predicting swarm dynamics.
• To accurately predict phenomena beyond mean-field predictions, such as unstable oscillations and bistability.

Main Methods:

• Developed a general model for time-delayed interactions in mobile-agent swarms.
• Conducted an exact stability analysis of primary swarming patterns.
• Identified relevant spatiotemporal modes for accurate dynamic prediction.

Main Results:

• Accurately predicted unstable oscillations beyond mean-field dynamics.
• Demonstrated accurate prediction of bistability in large swarms.
• Validated the capability to predict complex swarm behaviors influenced by time delays.

Conclusions:

• An exact stability analysis provides a more accurate understanding of delay-coupled swarm dynamics.
• This approach enhances the prediction and control of mobile robot swarms.
• Lays the groundwork for direct comparisons with experimental robotics findings.