The effects of within-neuron degree correlations in networks of spiking neurons

Abstract

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.

To appear in Biological Cybernetics

References in corpus (3)

• Scale-free brain functional networks
• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Mean field theory of assortative networks of phase oscillators

Cited by in corpus (5)

• Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review
• Pulse shape and voltage-dependent synchronization in spiking neuron networks
• Global and Local Reduced Models for Interacting, Heterogeneous Agents
• The effects of degree distributions in random networks of Type-I neurons
• Explosive behaviour in networks of Winfree oscillators