4-2018

Honors Thesis

Degree Name

Bachelors of Science (BS)

Mathematics

Junping Shi

Donald Campbell

Ryan Vinroot

Abstract

The topic of matrix stability is very important for determining the stability of solutions to systems of differential equations. We examine several problems in the field of matrix stability, including minimal conditions for a $7\times7$ matrix sign pattern to be potentially stable, and applications of sign patterns to the study of Turing instability in the $3\times3$ case. Furthermore, some of our work serves as a model for a new method of approaching similar problems in the future.

COinS