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Critical transition for colliding swarms.
Jason Hindes1, Victoria Edwards1,2, M Ani Hsieh2
1U.S. Naval Research Laboratory, Washington, DC 20375, USA.
Physical Review. E
|July 17, 2021
Summary
We developed a new model to predict when colliding swarms will mill. This analytical method accurately forecasts critical interaction parameters for swarm dynamics, validated by simulations.
Area of Science:
- Physics
- Robotics
- Biology
- Complex Systems
Background:
- Swarming behavior in mobile agents is crucial across disciplines.
- Interactions between multiple swarms can generate complex spatiotemporal patterns.
- Understanding swarm-on-swarm dynamics, especially collisions, is an emerging research area.
Purpose of the Study:
- To develop an analytical model for predicting milling states in colliding swarms.
- To identify the critical parameters governing swarm-on-swarm interaction dynamics.
- To extend numerical insights into the scattering of nonlinear, colliding swarms.
Main Methods:
- Developed a self-propelled, rigid-body approximation for colliding swarms.
- Assumed swarms oscillate near a limit cycle post-collision, maintaining uniform density.
- Analyzed the critical interaction coupling predicting scattering versus milling states.
Main Results:
- Predicted the critical swarm-on-swarm interaction coupling for milling.
- Demonstrated this critical coupling is a function of physical swarm parameters.
- Showed the critical coupling provides a lower bound for all impact parameters, including head-on collisions.
- Identified the critical coupling with a saddle-node bifurcation in the uniform density approximation.
Conclusions:
- The developed analytical method accurately predicts critical parameters for colliding swarm behavior.
- The rigid-body approximation provides a robust framework for understanding swarm-on-swarm interactions.
- Results align with both small and large multiagent simulations, validating the model.
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