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Signal propagation and linear response in the delay Vicsek model
Daniel Geiß1,2, Klaus Kroy1, Viktor Holubec3
1Institute for Theoretical Physics, University of Leipzig, 04103 Leipzig, Germany.
Physical Review. E
|December 23, 2022
Summary
Time delays in swarm interactions hinder leader following but improve stability. Longer delays and higher speeds promote ballistic information spread in swarms, impacting collective behavior.
Area of Science:
- Collective behavior
- Swarm intelligence
- Nonlinear dynamics
Background:
- Sensation-action retardation is a fundamental biological limitation.
- The Vicsek model is a key framework for studying swarm dynamics.
Purpose of the Study:
- To investigate the impact of time delays on swarm behavior within the Vicsek model.
- To analyze how delays affect leader following, stability, and information propagation.
Main Methods:
- Simulations of the Vicsek model with discrete time delays.
- Analysis of swarm alignment, stability, and information spreading dynamics.
- Mathematical analysis of the order parameter and its response to bias and delays.
Main Results:
- Time delays decrease leader-following ability but enhance swarm stability against perturbations.
- Increased speed and delay duration favor ballistic over diffusive information propagation.
- Order parameter scales linearly with bias and inversely with delay for short delays; variance saturates.
- Linear response fails when orientation conservation is violated.
Conclusions:
- Time delays introduce a trade-off between responsiveness and stability in swarms.
- Delay dynamics significantly influence information flow and collective decision-making.
- The Vicsek model with delays provides insights into real-world biological and artificial swarm systems.
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