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

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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.

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Acknowledgements

This work is partially supported by the Marsden Fund Council from Government funding, managed by Royal Society Te Apārangi. We thank Andrew Punnett and Marti Anderson for useful conversations about copulas and Shawn Means for comments on the manuscript. We also thank the referees for their helpful comments which improved the paper.

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Correspondence to Carlo R. Laing.

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Communicated by Benjamin Lindner.

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Laing, C.R., Bläsche, C. The effects of within-neuron degree correlations in networks of spiking neurons. Biol Cybern 114, 337–347 (2020). https://doi.org/10.1007/s00422-020-00822-0

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