  The counter-intuitive phenomenon of coherence resonance describes a
non-monotonic behavior of the regularity of noise-induced oscillations in the
excitable regime, leading to an optimal response in terms of regularity of the
excited oscillations for an intermediate noise intensity. We study this
phenomenon in populations of FitzHugh-Nagumo (FHN) neurons with different
coupling architectures. For networks of FHN systems in excitable regime,
coherence resonance has been previously analyzed numerically. Here we focus on
an analytical approach studying the mean-field limits of the locally and
globally coupled populations. The mean-field limit refers to the averaged
behavior of a complex network as the number of elements goes to infinity. We
derive a mean-field limit approximating the locally coupled FHN network with
low noise intensities. Further, we apply mean-field approach to the globally
coupled FHN network. We compare the results of the mean-field and network
frameworks for coherence resonance and find a good agreement in the globally
coupled case, where the correspondence between the two approaches is
sufficiently good to capture the emergence of anticoherence resonance. Finally,
we study the effects of the coupling strength and noise intensity on coherence
resonance for both the network and the mean-field model.
