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Simple rules for collective motion in groups of agents, like fish or robots, are sufficient for stable spatial ordering. Noise and delays impact order, with delays being more disruptive than random errors.

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Area of Science:

  • Collective behavior
  • Complex systems
  • Robotics

Background:

  • Many biological and artificial systems exhibit collective motion.
  • Agents in groups avoid collisions and maintain cohesion.
  • Existing models often include complex interaction rules.

Purpose of the Study:

  • To identify minimal sufficient rules for stable collective motion.
  • To investigate the impact of noise and delays on group ordering.
  • To develop a simplified model for understanding large flock dynamics.

Main Methods:

  • Developed a minimal, isotropic, continuous-time, continuous-space model.
  • Simulated agents with preferred speed, radial repulsion, and long-range attraction.
  • Analyzed the effects of varying noise levels and interaction delays.

Main Results:

  • Preferred speed, repulsion, and attraction are sufficient for stable ordering.
  • Noise and delays significantly affect ordering, with delays being more detrimental.
  • The transition between ordered and disordered states due to noise is rapid.
  • Emergence and disappearance rates of order vary with interaction delays.

Conclusions:

  • A simple set of rules governs stable collective motion in 3D.
  • The model provides insights into managing large flocks with inherent noise and delays.
  • Understanding these minimal rules is key to predicting and controlling group behavior.