Effects of the network structure and coupling strength on the noise-induced response delay of a neuronal network

The Hodgkin–Huxley (H–H) neuron model driven by stimuli just above threshold shows a noise-induced response delay with respect to time to the first spike for a certain range of noise strengths, an effect called “noise delayed decay” (NDD). We study the response time of a network of coupled H–H neurons, and investigate how the NDD can be affected by the connection topology of the network and the coupling strength. We show that the NDD effect exists for weak and intermediate coupling strengths, whereas it disappears for strong coupling strength regardless of the connection topology. We also show that although the network structure has very little effect on the NDD for a weak coupling strength, the network structure plays a key role for an intermediate coupling strength by decreasing the NDD effect with the increasing number of random shortcuts, and thus provides an additional operating regime, that is absent in the regular network, in which the neurons may also exploit a spike time code.