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Filtering by: Subject Investments -- Mathematical models Degree Level Bachelor's

The Mathematics of Critical Shifts in Ecological Networks with Alternative Stable State Theory, A Potential Framework for Early Warning Indicators

Creator:

Kupperman, Michael D.

Abstract:

A long running problem in mathematical biology is the prediction of extinction events, a specialized case of the larger global stability problem found in differential equations and dynamical systems theory. A central technical question is how to introduce the randomness observed in real ecological systems not accounted for in deterministic...

Resource Type:

Honors College Thesis

Full Text:

biology have emphasized the mathematical and ecological relationships between model parameters, rather
Localized Structures in a Diffusive Run-and-Tumble Model of Myxococcus xanthus

Creator:

Flynn, Patrick Thomas

Abstract:

The bacteria Myxococcus xanthus clusters into fruiting bodies in the absence of food. The movement of M. xanthus has three aspects: self-propulsion (run), change of direction due to collision (tumble), and Brownian fluctuations in movement. We propose a minimalist PDE model for the concentrations of left and right moving agents...

Resource Type:

Honors College Thesis

Full Text:

describe the rippling behavior. With this minimalist mathematical model, we demonstrate the existence and