Kathleen Hoffman

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Singularly perturbed systems of ordinary differential equations arise in many biological, physical and chemical systems. We present an example of a singularly perturbed system of ordinary differential equations that arises as a model of the electrical potential across the cell membrane of a neuron. We describe two periodic solutions of this example that(More)
Using phase response curves and averaging theory, we derive phase oscillator models for the lamprey central pattern generator from two biophysically-based segmental models. The first one relies on network dynamics within a segment to produce the rhythm, while the second contains bursting cells. We study intersegmental coordination and show that the former(More)
The forced van der Pol oscillator has been the focus of scientific scrutiny for almost a century, yet its global bifurcation structure is still poorly understood. In this paper, we present a hybrid system consisting of the dynamics of the trajectories on the slow manifold coupled with “jumps” at the folds in the critical manifold to approximate the fast(More)
This is the second in a series of papers about the dynamics of the forced van der Pol oscillator [J. Guckenheimer, K. Hoffman, and W. Weckesser, SIAM J. Appl. Dyn. Syst., 2 (2003), pp. 1–35]. The first paper described the reduced system, a two dimensional flow with jumps that reflect fast trajectory segments in this vector field with two time scales. This(More)
OBJECTIVES To identify the strength limiting flaws in in vitro test specimens of a fine-grained feldspathic dental porcelain. METHODS Four-point flexural strengths were measured for 26 test specimens. The fracture origin site of every test specimen was studied using stereoptical and scanning electron microscopy. A fractographically labeled Weibull(More)
The emerging need to view improved quality of life as an outcome measure from human service programs was described, and a Quality of Life Index was proposed that can be used as either an outcome measure or the criterion for the goodness-of-fit between persons and their environments. Data were presented from 685 adult clients within Nebraska's Community(More)
The posterior thalamic nucleus (PO) is a higher order nucleus heavily implicated in the processing of somatosensory information. We have previously shown in rodent models that activity in PO is tightly regulated by inhibitory inputs from a GABAergic nucleus known as the zona incerta (ZI). The level of incertal inhibition varies under both physiological and(More)
Hairston, Slobodkin, and Smith conjectured that top down forces act on food chains, which opposed the previously accepted theory that bottom up forces exclusively dictate the dynamics of populations. We model food chains using the Lotka-Volterra predation model and derive sustainability constants which determine which species will persist or go extinct.(More)
Redesigning undergraduate biology courses to integrate quantitative reasoning and skill development is critical to prepare students for careers in modern medicine and scientific research. In this paper, we report on the development, implementation, and assessment of stand-alone modules that integrate quantitative reasoning into introductory biology courses.(More)