From individual to collective behaviour of coupled velocity jump processes: A locust example

Radek Erban, Jan Haskovec

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

A class of stochastic individual-based models, written in terms of coupled velocity jump processes, is presented and analysed. This modelling approach incorporates recent experimental findings on the behaviour of locusts. It exhibits nontrivial dynamics with a pitchfork bifurcation and recovers the observed group directional switching. Estimates of the expected switching times, in terms of the number of individuals and values of the model coefi-cients, are obtained using the corresponding Fokker-Planck equation. In the limit of large populations, a system of two kinetic equations (with nonlocal and nonlinear right hand side) is derived and analyzed. The existence of its solutions is proven and the system's long-time behaviour is investigated. Finally, a first step towards the mean field limit of topological interactions is made by studying the efiect of shrinking the interaction radius in the individual-based model. © American Institute of Mathematical Sciences.
Original languageEnglish (US)
Pages (from-to)817-842
Number of pages26
JournalKinetic and Related Models
Volume5
Issue number4
DOIs
StatePublished - Nov 2012

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation

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