Graduation Year
2006
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Jon T. Jacobsen
Reader 2
Pablo Padilla (Universidad Nacional Autónoma de México)
Abstract
Turing theory plays an important role in real biological pattern formation problems, such as solid tumor growth and animal coat patterns. To understand how patterns form and develop over time due to growth, we consider spatiotemporal patterns, in particular Turing patterns, for reaction diffusion systems on growing surfaces with curvature. Of particular interest is isotropic growth of the sphere, where growth of the domain occurs in the same proportion in all directions. Applying a modified linear stability analysis and a separation of timescales argument, we derive the necessary and sufficient conditions for a diffusion driven instability of the steady state and for the emergence of spatial patterns. Finally, we explore these results using numerical simulations.
Recommended Citation
Gjorgjieva, Julijana, "Turing Pattern Dynamics for Spatiotemporal Models with Growth and Curvature" (2006). HMC Senior Theses. 181.
https://scholarship.claremont.edu/hmc_theses/181
Picture of Julijana Gjorgjieva
julegjor-2006-prop.pdf (64 kB)
Thesis Proposal
