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

Handle URI:
http://hdl.handle.net/10754/562394
Title:
From individual to collective behaviour of coupled velocity jump processes: A locust example
Authors:
Erban, Radek; Haskovec, Jan
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.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
American Institute of Mathematical Sciences (AIMS)
Journal:
Kinetic and Related Models
Issue Date:
Nov-2012
DOI:
10.3934/krm.2012.5.817
ARXIV:
arXiv:1104.2584
Type:
Article
ISSN:
19375093
Sponsors:
This publication was based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). JH acknowledges the financial support provided by the FWF project Y 432-N15. The research leading to these results has received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013)/ ERC grant agreement n<SUP>o</SUP> 239870. RE would also like to thank Somerville College, University of Oxford, for a Fulford Junior Research Fellowship; Brasenose College, University of Oxford, for a Nicholas Kurti Junior Fellowship; the Royal Society for a University Research Fellowship; and the Leverhulme Trust for a Philip Leverhulme Prize. This prize money was used to support research visits of JH to Oxford. Both authors would like to thank to the Isaac Newton Institute for Mathematical Sciences in Cambridge (UK), where they worked together during the program "Partial Differential Equations in Kinetic Theories". The authors also acknowledge several interesting discussions and valuable hints provided by Jan Vybiral (Technical University Berlin) and Christian Schmeiser (University of Vienna).
Additional Links:
http://arxiv.org/abs/arXiv:1104.2584v1
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorErban, Radeken
dc.contributor.authorHaskovec, Janen
dc.date.accessioned2015-08-03T10:03:39Zen
dc.date.available2015-08-03T10:03:39Zen
dc.date.issued2012-11en
dc.identifier.issn19375093en
dc.identifier.doi10.3934/krm.2012.5.817en
dc.identifier.urihttp://hdl.handle.net/10754/562394en
dc.description.abstractA 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.en
dc.description.sponsorshipThis publication was based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). JH acknowledges the financial support provided by the FWF project Y 432-N15. The research leading to these results has received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013)/ ERC grant agreement n<SUP>o</SUP> 239870. RE would also like to thank Somerville College, University of Oxford, for a Fulford Junior Research Fellowship; Brasenose College, University of Oxford, for a Nicholas Kurti Junior Fellowship; the Royal Society for a University Research Fellowship; and the Leverhulme Trust for a Philip Leverhulme Prize. This prize money was used to support research visits of JH to Oxford. Both authors would like to thank to the Isaac Newton Institute for Mathematical Sciences in Cambridge (UK), where they worked together during the program "Partial Differential Equations in Kinetic Theories". The authors also acknowledge several interesting discussions and valuable hints provided by Jan Vybiral (Technical University Berlin) and Christian Schmeiser (University of Vienna).en
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)en
dc.relation.urlhttp://arxiv.org/abs/arXiv:1104.2584v1en
dc.subjectCollective behaviouren
dc.subjectDensitydependent directional switchingen
dc.subjectKinetic equation.en
dc.subjectStochastic individual-based modelen
dc.titleFrom individual to collective behaviour of coupled velocity jump processes: A locust exampleen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalKinetic and Related Modelsen
dc.contributor.institutionUniv Oxford, Math Inst, Oxford OX1 3LB, Englanden
dc.identifier.arxividarXiv:1104.2584en
kaust.authorHaskovec, Janen
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