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
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:AEU.10048/1727 |
| Date | 06 1900 |
| Creators | Wong, Rita |
| Contributors | De 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 Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 2472598 bytes, application/pdf |
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