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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.