Consequences of Dale's law on the stability-complexity relationship of random neural networks

J. R. Ipsen and A. D. H. Peterson
Phys. Rev. E 101, 052412 – Published 28 May 2020

Abstract

In the study of randomly connected neural network dynamics there is a phase transition from a simple state with few equilibria to a complex state characterized by the number of equilibria growing exponentially with the neuron population. Such phase transitions are often used to describe pathological brain state transitions observed in neurological diseases such as epilepsy. In this paper we investigate how more realistic heterogeneous network structures affect these phase transitions using techniques from random matrix theory. Specifically, we parametrize the network structure according to Dale's law and use the Kac-Rice formalism to compute the change in the number of equilibria when a phase transition occurs. We also examine the condition where the network is not balanced between excitation and inhibition causing outliers to appear in the eigenspectrum. This enables us to compute the effects of different heterogeneous network connectivities on brain state transitions, which can provide insights into pathological brain dynamics.

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  • Received 29 July 2019
  • Revised 17 March 2020
  • Accepted 8 April 2020

DOI:https://doi.org/10.1103/PhysRevE.101.052412

©2020 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsPhysics of Living Systems

Authors & Affiliations

J. R. Ipsen*

  • ARC Centre of Excellence for Mathematical and Statistical Frontiers, School of Mathematics and Statistics, University of Melbourne, 3010 Parkville, Victoria, Australia

A. D. H. Peterson

  • Graeme Clarke Institute, University of Melbourne, 3053 Carlton, Victoria, Australia and Department of Medicine, St. Vincent's Hospital, University of Melbourne, 3065 Fitzroy, Victoria, Australia

  • *jesper.ipsen@unimelb.edu.au
  • peterson@unimelb.edu.au

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Vol. 101, Iss. 5 — May 2020

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