Julijana Gjorgjieva
Harvey Mudd College Mathematics 2006
Turing Pattern Dynamics for Spatiotemporal
Models with Growth and Curvature
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.