| Summary: | Neuronal network models often assume a fixed probability of connectionbetween neurons. This assumption leads to random networks withbinomial in-degree and out-degree distributions which are relatively narrow. Here I study the effect of broaddegree distributions on network dynamics by interpolating between abinomial and a truncated powerlaw distribution for the in-degree andout-degree independently. This is done both for an inhibitory network(I network) as well as for the recurrent excitatory connections in anetwork of excitatory and inhibitory neurons (EI network). In bothcases increasing the width of the in-degree distribution affects theglobal state of the network by driving transitions betweenasynchronous behavior and oscillations. This effect is reproduced ina simplified rate model which includes the heterogeneity in neuronalinput due to the in-degree of cells. On the other hand, broadeningthe out-degree distribution is shown to increase the fraction ofcommon inputs to pairs of neurons. This leads to increases in theamplitude of the cross-correlation (CC) of synaptic currents. In thecase of the I network, despite strong oscillatory CCs in the currents, CCs of the membrane potential are low due to filtering and reset effects, leading to very weak CCs of the spikecount. In the asynchronous regime ofthe EI network, broadening the out-degree increases the amplitude ofCCs in the recurrent excitatory currents, while CC of the totalcurrent is essentially unaffected as are pairwise spikingcorrelations. This is due to a dynamic balance between excitatoryand inhibitory synaptic currents. In the oscillatory regime, changesin the out-degree can have a large effect on spiking correlations andeven on the qualitative dynamical state of the network.
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