Turing patterns on growing spheres: the exponential case

Pages: 436 - 445, Issue Special, September 2007

 Abstract        Full Text (790.6K)              

Julijana Gjorgjieva - Centre for Mathematical Sciences, Wilberforce Rd, Cambridge CB3 0WA, United Kingdom (email)
Jon Jacobsen - Harvey Mudd College, Mathematics Department, 301 Platt Blvd, Claremont, CA 91711, United States (email)

Abstract: We consider Turing patterns for reaction-diffusion systems on the surface of a growing sphere. In particular, we are interested in the effect of dynamic growth on the pattern formation. We consider exponential isotropic growth of the sphere and perform a linear stability analysis and compare the results with numerical simulations.

Keywords:  Pattern formation, Turing, reaction-diffusion, sphere, growth.
Mathematics Subject Classification:  Primary: 35K57; Secondary: 37N25, 92C15.

Received: September 2006;      Revised: April 2007;      Published: September 2007.