  The onset of pulse propagation is studied in a reaction-diffusion (RD) model
with control by augmented transmission capability that is provided either along
nonlocal spatial coupling or by time-delayed feedback. We show that traveling
pulses occur primarily as solutions to the RD equations while augmented
transmission changes excitability. For certain ranges of the parameter
settings, defined as weak susceptibility and moderate control, respectively,
the hybrid model can be mapped to the original RD model. This results in an
effective change of RD parameters controlled by augmented transmission. Outside
moderate control parameter settings new patterns are obtained, for example
step-wise propagation due to delay-induced oscillations. Augmented transmission
constitutes a signaling system complementary to the classical RD mechanism of
pattern formation. Our hybrid model combines the two major signaling systems in
the brain, namely volume transmission and synaptic transmission. Our results
provide insights into the spread and control of pathological pulses in the
brain.
