  In two-dimensional reaction-diffusion systems, local curvature perturbations
in the shape of traveling waves are typically damped out and disappear in the
course of time. If, however, the inhibitor diffuses much faster than the
activator, transversal instabilities can arise, leading from flat to folded,
spatio-temporally modulated wave shapes and to spreading spiral turbulence. For
experimentally relevant parameter values, the photosensitive
Belousov-Zhabotinsky reaction (PBZR) does not exhibit transversal wave
instabilities. Here, we propose a mechanism to artificially induce these
instabilities via a wave shape dependent spatio-temporal feedback loop, and
study the emerging wave patterns. In numerical simulations with the modified
Oregonator model for the PBZR using experimentally realistic parameter values
we demonstrate the feasibility of this control scheme. Conversely, in a
piecewise-linear version of the FitzHugh-Nagumo model transversal instabilities
and spiral turbulence in the uncontrolled system are shown to be suppressed in
the presence of control, thereby stabilising flat wave propagation.
