DOI: 10.7554/elife.88777.3 ISSN: 2050-084X

Structural constraints on the emergence of oscillations in multi-population neural networks

Jie Zang, Shenquan Liu, Pascal Helson, Arvind Kumar
  • General Immunology and Microbiology
  • General Biochemistry, Genetics and Molecular Biology
  • General Medicine
  • General Neuroscience

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.

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