  The effects of nonlocal and reflecting connectivity are investigated in
coupled Leaky Integrate-and-Fire (LIF) elements, which assimilate the exchange
of electrical signals between neurons. Earlier investigations have demonstrated
that non-local and hierarchical network connectivity often induces complex
synchronization patterns and chimera states in systems of coupled oscillators.
In the LIF system we show that if the elements are non-locally linked with
positive diffusive coupling in a ring architecture the system splits into a
number of alternating domains. Half of these domains contain elements, whose
potential stays near the threshold, while they are interrupted by active
domains, where the elements perform regular LIF oscillations. The active
domains move around the ring with constant velocity, depending on the system
parameters. The idea of introducing reflecting non-local coupling in LIF
networks originates from signal exchange between neurons residing in the two
hemispheres in the brain. We show evidence that this connectivity induces novel
complex spatial and temporal structures: for relatively extensive ranges of
parameter values the system splits in two coexisting domains, one domain where
all elements stay near-threshold and one where incoherent states develop with
multileveled mean phase velocity distribution.
