Large scale dynamics of the persistent turning walker model of fish behavior

Pierre Degond, Sébastien Motsch

Research output: Contribution to journalArticlepeer-review

130 Scopus citations


This paper considers a new model of individual displacement, based on fish motion, the so-called Persistent Turning Walker (PTW) model, which involves an Ornstein-Uhlenbeck process on the curvature of the particle trajectory. The goal is to show that its large time and space scale dynamics is of diffusive type, and to provide an analytic expression of the diffusion coefficient. Two methods are investigated. In the first one, we compute the large time asymptotics of the variance of the individual stochastic trajectories. The second method is based on a diffusion approximation of the kinetic formulation of these stochastic trajectories. The kinetic model is a Fokker-Planck type equation posed in an extended phase-space involving the curvature among the kinetic variables. We show that both methods lead to the same value of the diffusion constant. We present some numerical simulations to illustrate the theoretical results.

Original languageEnglish (US)
Pages (from-to)989-1021
Number of pages33
JournalJournal of Statistical Physics
Issue number6
StatePublished - Jun 2008
Externally publishedYes


  • Asymptotic analysis
  • Diffusion approximation
  • Fish behavior
  • Individual based model
  • Kinetic Fokker-Planck equation
  • Ornstein-Uhlenbeck process
  • Persistent Turning Walker model

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


Dive into the research topics of 'Large scale dynamics of the persistent turning walker model of fish behavior'. Together they form a unique fingerprint.

Cite this