Examples of considered network topologies. For clarity only a excerpt of the whole network is presented in each panel. (a) Diffusively coupled network characterized by . Each vertex is directly connected only to its four nearest neighbors, hence having connectivity . (b) Realization of small-world topology via random rewiring of a certain fraction of links, constrained only by the requirement that the initial connectivity of each unit must be preserved.
Characteristic snapshots of the spatial profile of obtained for (a) , (b) , and (c) . For the intermediate value of the spatial dynamics is clearly most coherent, exhibiting ordered circular waves propagating through the spatial grid.
The spatial structure function of obtained for (a) , (b) , and (c) . For the intermediate value of the characteristic waterfall-like outlay of is evident, indicating the existence of a preferred spatial frequency of noise-induced excitatory events in the medium. Note that only an excerpt of the whole plane is shown in all panels.
Evidence for spatial coherence resonance in the studied HH medium. (a) The circular averages of structure functions presented in Fig. 3 . The dashed vertical line at marks the spatial frequency of excitatory events that is resonantly enhanced by an intermediate level of additive Gaussian noise. (b) The signal to noise (SNR) ratio in dependence on (the curve is just a guide to the eye).
Characteristic snapshots of the spatial profile of obtained at the optimal value of for (a) , (b) , and (c) .
Evidence for decoherence of the spatial dynamics in the studied HH medium with small-world topology. (a) The signal to noise ratio (SNR) in dependence on for different . (b) SNR in dependence on by the optimal denoted by a dashed vertical line in panel (a). Inset features the circular average of the structure function for the optimal and three different values of , corresponding to the three snapshots presented in Fig. 5 .
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