Open Access Senior Thesis
Bachelor of Science
Jon T. Jacobsen
Pablo Padilla (Universidad Nacional Autónoma de México)
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.
Gjorgjieva, Julijana, "Turing Pattern Dynamics for Spatiotemporal Models with Growth and Curvature" (2006). HMC Senior Theses. 181.