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 individualbased 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 FokkerPlanck 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 longtime 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 individualbased 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 07:44 
Last Modified:  29 May 2015 18:51 
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