Pattern formation in reaction diffusion models <P>

In this talk, I will discuss results for pattern formation in
reaction-diffusion models for chemical dynamics which often arise in
the field of biology. In particular, a 1952 discovery of Turing showed
that a near-equilibrium mixture of chemical reactants could have
diffusion-driven pattern formation. I will describe the mathematical
nature of this pattern formation, as well as showing numerical results
for both pure reaction-diffusion equations, and equations with
non-local interactions, motivated by neuronal pattern forming systems
seen in recent experiments by my collaborators.