Structural constraints on the emergence of oscillations in multi-population neural networks
Abstract
Oscillations arise in many real-world systems and are associated with both functional and dysfunctional states. Whether a network can oscillate can be estimated if we know the strength of interaction between nodes. But in real-world networks (in particular in biological networks) it is usually not possible to know the exact connection weights. Therefore, it is important to determine the structural properties of a network necessary to generate oscillations. Here, we provide a proof that uses dynamical system theory to prove that an odd number of inhibitory nodes and strong enough connections are necessary to generate oscillations in a single cycle threshold-linear network. We illustrate these analytical results in a biologically plausible network with either firing-rate based or spiking neurons. Our work provides structural properties necessary to generate oscillations in a network. We use this knowledge to reconcile recent experimental findings about oscillations in basal ganglia with classical findings.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2023
- DOI:
- 10.48550/arXiv.2302.14157
- arXiv:
- arXiv:2302.14157
- Bibcode:
- 2023arXiv230214157Z
- Keywords:
-
- Quantitative Biology - Neurons and Cognition
- E-Print:
- Main text: 30 pages, 5 Figures. Supplementary information: 20 pages, 9 Figures. Supplementary Information is integrated in the main file