Field-theoretic approach to study a class of reaction-diffusion models

We present a field-theoretic derivation of a class of models of reaction-diffusion systems of which the Gray-Scott model is a special case. Numerical studies of some of these models have shown the phenomena of self replicating spots and stripes [1,2]. More recently, a field-theoretic approach was used to study the noise driven phase transitions in Gray-Scott model. [3] We use our field theory approach to analytically study the dynamics of the spots for a general class of models and compare analytics with numerical results.
[1] J. E. Pearson, Science 261, 189 (1993).
[2] W. N. Reynolds, S. Ponce-Dawson, and J. E. Pearson, Phys. Rev. E 56, 185 (1997).
[3] F. Cooper, G. Ghoshal, and J. Perez-Mercader, Phys. Rev. Lett. 111, 044101 (2013).