  Spatial coherence resonance in a spatially extended system that is locally
modeled by Hodgkin-Huxley (HH) neurons is studied in this paper. We focus on
the ability of additive temporally and spatially uncorrelated Gaussian noise to
extract a particular spatial frequency of excitatory waves in the medium,
whereby examining also the impact of diffusive and small-world network topology
determining the interactions amongst coupled HH neurons. We show that there
exists an intermediate noise intensity that is able to extract a characteristic
spatial frequency of the system in a resonant manner provided the latter is
diffusively coupled, thus indicating the existence of spatial coherence
resonance. However, as the diffusive topology of the medium is relaxed via the
introduction of shortcut links introducing small-world properties amongst
coupled HH neurons, the ability of additive Gaussian noise to evoke ordered
excitatory waves deteriorates rather spectacularly, leading to the decoherence
of the spatial dynamics and with it related absence of spatial coherence
resonance. In particular, already a minute fraction of shortcut links suffices
to substantially disrupt coherent pattern formation in the examined system.
