Brownian motion and swarm dynamics

Eugene Khmelnitsky*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


This chapter considers the model of the swarm dynamics by the use of Langevin and Fokker-Plank equations. These equations allow the description the swarm motion using the methods of statistical physics. The interactions between the environment and the Brownian particle results in three forces that act on the Brownian particle: a damping force, a force associated with the exogenous fields, and a fluctuating force. The forces affect the dynamics of the location and speed of the Brownian particle, as given in the one-dimensional Langevin equation. The dynamics of speed follow the Brownian motion, growing linearly with time. The chapter presents examples to show that the presence of the damping force restricts the motion in such a way that the dependence of the location variance on time drops down from a power of three to linearly proportional, and the speed variance loses its dependence on time at all.

Original languageEnglish
Title of host publicationAutonomous Mobile Robots and Multi-Robot Systems
Subtitle of host publicationMotion-Planning, Communication, and Swarming
EditorsEugene Kagan, Nir Shvalb, Irad Ben-Gal
Number of pages12
ISBN (Electronic)9781119213154, 9781119213178, 9781119213161
ISBN (Print)9781119212867
StatePublished - 6 Sep 2019


  • Brownian motion
  • Damping force
  • Exogenous fields
  • Fluctuating force
  • Fokker-Plank equations
  • Langevin equation
  • Statistical physics
  • Swarm dynamics


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