Birth and destruction of collective oscillations in a network of two populations of coupled type 1 neurons

Benjamin Jüttner, Christian Henriksen, Erik A. Martens*

*Corresponding author for this work

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Abstract

We study the macroscopic dynamics of large networks of excitable type 1 neurons composed of two populations interacting with disparate but symmetric intra- and inter-population coupling strengths. This nonuniform coupling scheme facilitates symmetric equilibria, where both populations display identical firing activity, characterized by either quiescent or spiking behavior, or asymmetric equilibria, where the firing activity of one population exhibits quiescent but the other exhibits spiking behavior. Oscillations in the firing rate are possible if neurons emit pulses with non-zero width but are otherwise quenched. Here, we explore how collective oscillations emerge for two statistically identical neuron populations in the limit of an infinite number of neurons. A detailed analysis reveals how collective oscillations are born and destroyed in various bifurcation scenarios and how they are organized around higher codimension bifurcation points. Since both symmetric and asymmetric equilibria display bistable behavior, a large configuration space with steady and oscillatory behavior is available. Switching between configurations of neural activity is relevant in functional processes such as working memory and the onset of collective oscillations in motor control.

Original languageEnglish
Article number023141
JournalChaos
Volume31
Issue number2
Number of pages13
ISSN1054-1500
DOIs
Publication statusPublished - 1 Feb 2021

Bibliographical note

Funding Information:
The authors would like to thank C. Bick and B. Pietras for helpful discussions, and A. Torcini and P. So for helpful correspondence. Research conducted by B.J. was partially supported by funding from the EU-COST Technical University of Denmark.

Publisher Copyright:
© 2021 Author(s).

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