  The effects of nonlocal and reflecting connectivities have been previously
investigated in coupled Leaky Integrate-and-Fire (LIF) elements, which
assimilate the exchange of electrical signals between neurons. In this work we
investigate the effect of diagonal coupling inspired by findings in brain
neuron connectivity. Multi-chimera states are reported both for the simple
diagonal and combined nonlocal-diagonal connectivities and we determine the
range of optimal parameter regions where chimera states appear. Overall, the
measures of coherence indicate that as the coupling range increases (below
all-to-all coupling) the emergence of chimera states is favoured and the mean
phase velocity deviations between coherent and incoherent regions become more
prominent. A number of novel synchronization phenomena are induced as a result
of the combined connectivity. We record that for coupling strengths $\sigma <
1$ the synchronous regions have mean phase velocities lower than the
asynchronous, while the opposite holds for $\sigma > 1$. In the intermediate
regime, $\sigma \sim 1$, the oscillators have common mean phase velocity (i.e.,
are frequency-locked) but different phases (i.e., they are phase-asynchronous).
Solitary states are recorded for small values of the coupling strength, which
grow into chimera states as the coupling strength increases.We determine
parameter values where the combined effects of nonlocal-diagonal coupling
generate chimera states with two different levels of synchronous domains
mediated by asynchronous regions.
