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Study of animal movement and group formation with a Lagrangian model

Animal group formation has often been studied by mathematical biologists through PDE models, producing
classical results like traveling and stationary waves. Recently, Eftimie et al. introduced a 1-D PDE model
that considers three social interactions between individuals in the relevant neighborhoods, specifically re-
pulsion, alignment, and attraction. It takes into account the orientation of the neighbors when consider-
ing if they can communicate. This has resulted in exciting new movement behaviors like zig-zag pulses,
breathers, and feathers. In this work, we translate the Eftimie model into a Lagrangian implementation.
Currently, the results from the Lagrangian formulations show many of the results displayed by Eftimie’s
original PDE model, producing patterns like the zig-zag, breather traveling, and stationary pulses. In addi-
tion, we model animal movement with an ODE approach to complete the investigation regarding the role of
direction-dependent communication mechanism in discrete-space. / Applied Mathematics

Identiferoai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:AEU.10048/1727
Date06 1900
CreatorsWong, Rita
ContributorsDe Vries, Gerda (Mathematical and Statistical Sciences), Jones, Kelvin (Physical Education and Recreation), Lewis, Mark (Mathematical and Statistical Sciences), Dawes, Adriana (Mathematical and Statistical Sciences)
Source SetsLibrary and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada
LanguageEnglish
Detected LanguageEnglish
TypeThesis
Format2472598 bytes, application/pdf

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