Mathematics Colloquia and Seminars
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Steady State Behavior of an Insect Outbreak: The use of dynamical systems methods in solving PDEsStudent-Run Applied & Math Seminar
|Speaker: ||Kevin Lamb, UC Davis|
|Location: ||2112 MSB|
|Start time: ||Wed, Oct 9 2013, 12:10PM|
In response to an outbreak in New Brunswick, Canada, Ludwig, et. al, began
a series of papers in 1978 detailing the population dynamics of Choristoneura fu-
miferana, the Spruce Budworm. In the rst paper, he and his colleagues developed
and analyzed a temporal model describing the density of a population of budworms.
This model is used in the second of his papers, published in 1979, in the study of a
spatial model. This spatial model is the focus of our discussion. The spatial model
is formulated as a partial di erential equation and can be studied without explicit
calculation of solutions. Ludwig employs rst integrals and bifurcation analysis to
study the critical patch size necessary to sustain an outbreak of budworms. We
focus more on the use of dynamical systems methods in studying the partial dif-
ferential equation rather than the results that Ludwig concluded in his research.
We also explore original research into the study and analysis of the steady-state
distributions resulting from the system.