The Mathematical Institute, University of Oxford, Eprints Archive

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

Erban, R. and Haskovec, J. (2011) From individual to collective behaviour of coupled velocity jump processes: a locust example. Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire . (Submitted)

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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 behaviour of locusts. It exhibits nontrivial dynamics with a “phase change” behaviour and recovers the observed group directional switching. Estimates of the expected switching times, in terms of number of individuals and values of the model coefficients, 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 effect of shrinking the interaction radius in the individual-based model when the number of individuals grows.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1167
Deposited By:Peter Hudston
Deposited On:14 May 2011 08:44
Last Modified:09 Feb 2012 14:05

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