Date of Final Oral Examination (Defense)

5-2012

Type of Culminating Activity

Thesis

Degree Title

Master of Science in Mathematics

Department

Mathematics

Major Advisor

Donna Calhoun, Ph.D.

Abstract

We explore a striped pattern generated by a general Turing model in three different geometries. We look at the square, disk, and hemisphere and make connections between the stripes in each spatial direction. In particular, we gain a greater understanding of when perfect stripes can be generated and what causes defects in their patterns. In this investigation, we look at the difference between the solutions due to the different domain shapes. In the end, we propose a reason why stripes from a reaction-diffusion system with zero-flux boundary conditions can be perfect on a square or hemisphere, but not on a disk.

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