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
focus are diffusion-induced instabilities, i.e., Turing instabilities.
present various theorems that make it possible to determine
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
Specific examples focus on well-stirred chemical reactors. The
coupled by diffusion-like mass transfer, and the kinetics is given by
Lengyel-Epstein model, a two-variable scheme for the chlorine dioxide-
iodine-malonic acid reaction.