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Flocking dynamics and pattern motion for the Cucker-Smale system with distributed delays.

Jingyi He1, Changchun Bao2, Le Li2

  • 1School of Mathematics and Statistics, Changsha University of Science and Technology, Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha 410114, China.

Mathematical Biosciences and Engineering : MBE
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Summary

This study introduces new Cucker-Smale systems with distributed delays to analyze flocking dynamics. New criteria are established for flocking behavior, even with non-normalized communication rates, using a driving force for pattern motion.

Keywords:
Cucker-Smale modeldistributed delayflocking behaviorpattern motion

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Area of Science:

  • Control Theory
  • Dynamical Systems
  • Collective Behavior

Background:

  • Cucker-Smale systems model flocking in multi-agent systems.
  • Distributed delays introduce complexity in modeling collective dynamics.
  • Measurement perspectives are crucial for analyzing real-world system behavior.

Purpose of the Study:

  • Develop a new class of Cucker-Smale systems incorporating distributed delays.
  • Establish sufficient criteria for flocking dynamics under general communication rates.
  • Incorporate a driving force for achieving prescribed pattern motion in delayed systems.

Main Methods:

  • Utilizing dissipative differential inequalities.
  • Applying a continuity argument for theoretical analysis.
  • Developing a delayed collective system with a driving force term.

Main Results:

  • New sufficient criteria for flocking dynamics are established.
  • The model accommodates general communication rates, including non-normalized ones.
  • Theoretical results are validated through examples and simulations.

Conclusions:

  • The proposed Cucker-Smale systems with distributed delays effectively model flocking dynamics.
  • The established criteria provide robust conditions for achieving flocking behavior.
  • The inclusion of a driving force enables controlled pattern formation in delayed multi-agent systems.