Localized Patterns in Homogeneous Networks of Diffusively Coupled Reactors

We study the influence of network topology on instabilities of the homogeneous
steady state of diffusively coupled, monostable nonlinear cells. A particular
focus are diffusion-induced instabilities, i.e., Turing instabilities. We
present various theorems that make it possible to determine analytically the
stability properties of networks with arbitrary topologies and general
monostable dynamics of the individual cells.   This work aims in particular to
determine those topologies that will give rise to localized stationary patterns.
Specific examples focus on well-stirred chemical reactors.  The reactors are
coupled by diffusion-like mass transfer, and the kinetics is given by the
Lengyel-Epstein model, a two-variable scheme for the chlorine dioxide-
iodine-malonic acid reaction.