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Modeling group formation and activity patterns in self-organizing communities of organisms
- Author / Creator
- Raluca A. Eftimie
In this thesis, we propose a general framework to model animal group formation and movement based on how individuals receive information from neighbors, and the amount of information received. In particular, we construct and
analyze a new one-dimensional nonlocal hyperbolic model for group formation,
with application to self-organizing collectives of animals in homogeneous environments. The model investigates the effects of nonlocal social interactions
(that is, attraction towards neighbors that are far away, repulsion from those
that are near by, and alignment with neighbors at intermediate distances) on
the emergence of group patterns. These nonlocal interactions can influence
individuals’ speed and turning behavior.
We demonstrate that this one-dimensional model can generate a wide range
of spatial and spatiotemporal patterns. In particular, depending on the assumptions regarding how individuals receive information, the model displays
at least 21 different patterns. Some of these patterns are classical, such as stationary pulses, traveling pulses, or traveling trains. However, the majority of
these patterns are novel, such as the patterns we call zigzag pulses and feathers. To investigate these patterns, we use numerical and analytical techniques
such as bifurcation theory, linear and nonlinear analysis.
This modeling framework presents a unitary approach for animal group
formation and movement. All the patterns obtained with other parabolic and
hyperbolic models existent in the literature can also be obtained with the
model we propose in this thesis. In addition to this, we obtain a variety of
new and interesting patterns.
- Graduation date
- Type of Item
- Doctor of Philosophy in Applied Mathematics
- This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.