  Transient wave forms in neural networks with diffusive and nonlocal coupling
have attracted particular interest because they may mediate recruitment of
healthy cortical tissue into a pathological state during migraine. To
investigate this process, we use a reaction-diffusion system of
inhibitor-activator type as a generic model of pathological wave propagation
and set it close to bifurcation in the sub-excitable regime. We report the
influence of various nonlocal connectivity schemes on wave propagation. Wave
propagation can be suppressed with cross coupling inhibitor and activator for
both positive and negative coupling strength K, depending on the connection
length d. The area in the parameter plane (d,K) where this control goal is
achieved resembles a Mexican-hat-type network connectivity. Our results suggest
that nonlocal synaptic transmission can control wave propagation, which may be
of therapeutic value.
