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Topological Characterization of Extinction in a Coupled Ricker Patch Model

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Author: Holman, Benjamin Robert
Advisor: Day, Sarah, 1975-
Committee Members: Shaw, Leah B.; Shi, Junping; Lewis, Robert Michael
Issued Date: 5/12/2011
Subjects: Computational Homology
Meta population
Ricker
Coupled Patch Model
Computational Topology
Spatial chaos
URI: http://hdl.handle.net/10288/13699
Description: Ecologists use Ricker patch models to study meta-population dynamics for populations undergoing growth and dispersal in a patchy environment. This project uses a modified model in which patch-wise extinction thresholds are used to model local extinction events. Computational homology is used to measure shifts in spatial patterns as extinction occurs and to quantify the ways in which dispersal rates affect pattern formation and degradation. Numerical simulations for certain parameters exhibit a decoupling of the system into small regions with periodic dynamics prior to extinction. Lastly, the existence of certain stable periodic orbits which affect population robustness are rigorously proven to exist.
Degree: Bachelors of Science in Mathematics


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