  We consider the effects of correlations between the in- and out-degrees of
individual neurons on the dynamics of a network of neurons. By using theta
neurons, we can derive a set of coupled differential equations for the expected
dynamics of neurons with the same in-degree. A Gaussian copula is used to
introduce correlations between a neuron's in- and out-degree and numerical
bifurcation analysis is used determine the effects of these correlations on the
network's dynamics. For excitatory coupling we find that inducing positive
correlations has a similar effect to increasing the coupling strength between
neurons, while for inhibitory coupling it has the opposite effect. We also
determine the propensity of various two- and three-neuron motifs to occur as
correlations are varied and give a plausible explanation for the observed
changes in dynamics.
