Functional motifs: a novel perspective on burst synchronization and regularization of neurons coupled via delayed inhibitory synapses

For one of the most common network motifs, an inhibitory neuron pair, we perform an extensive study of burst synchronization and the related phenomena applying the model of Rulkov maps coupled via delayed synapses. Instigated by the phase-plane analysis, that has the neuron switching between the noninteracting and the interacting map, it is demonstrated how the system evolution may be interpreted by means of the dynamical configurations of the motif, each represented by an extracted subgraph. Under the variation of the synaptic parameters, the probability of finding synchronized neurons in a given configuration is seen to reflect the way in which the anti-phase synchronization is eventually superseded by the synchronization in phase. Such an approach also provides a novel insight into regularization, characterizing the neuron bursting in either of these regimes. Looking into correlation of the two neurons’ bursting cycles we acquire a deeper understanding of the more sophisticated mechanisms by which the regularity in the time series is maintained. Further, it is examined whether introducing heterogeneity in the neuron or the synaptic parameters may prove advantageous over the homogeneous case with respect to burst synchronization.