Elsevier

Automatica

Volume 146, December 2022, 110653
Automatica

Structural characterization of oscillations in brain networks with rate dynamics☆

https://doi.org/10.1016/j.automatica.2022.110653Get rights and content
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Abstract

Among the versatile forms of dynamical patterns of activity exhibited by the brain, oscillations are one of the most salient and extensively studied, yet are still far from being well understood. In this paper, we provide various structural characterizations of the existence of oscillatory behavior in neural networks using a classical neural mass model of mesoscale brain activity called linear-threshold dynamics. Exploiting the switched-affine nature of this dynamics, we obtain various necessary and/or sufficient conditions on the network structure and its external input for the existence of oscillations in (i) two-dimensional excitatory–inhibitory networks (E-I pairs), (ii) networks with one inhibitory but arbitrary number of excitatory nodes, (iii) purely inhibitory networks with an arbitrary number of nodes, and (iv) networks of E-I pairs. Throughout our treatment, and given the arbitrary dimensionality of the considered dynamics, we rely on the lack of stable equilibria as a system-based proxy for the existence of oscillations, and provide extensive numerical results to support its tight relationship with the more standard, signal-based definition of oscillations in computational neuroscience.

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Erfan Nozari received his B.Sc. degree in Electrical Engineering-Control in 2013 from Isfahan University of Technology, Iran, received his Ph.D. in Mechanical Engineering and Cognitive Science in 2019 from University of California San Diego, and was subsequently a postdoctoral researcher in the University of Pennsylvania Department of Electrical and Systems Engineering. He is currently an assistant professor at the University of Riverside, California Department of Mechanical Engineering. He has been the (co)recipient of the 2019 IEEE Transactions on Control of Network Systems Outstanding Paper Award, the Best Student Paper Award from the 57th IEEE Conference on Decision and Control, the Best Student Paper Award from the 2018 American Control Conference, and the Mechanical and Aerospace Engineering Distinguished Fellowship Award from the University of California San Diego. His research interests include the applications of systems and control theory and machine learning in computational and theoretical neuroscience.

Robert Planas received his B.Sc. degrees in Mathematics and Aerospace Engineering in 2019 at Universidad Politécnica de Cataluña, Spain, while enrolled with the Centro de Formación Interdisciplinaria Superior (CFIS). In 2021 he graduated from the University of California, Irvine with a M.S. degree in Mechanical and Aerospace Engineering. His research interests include deep learning, system modeling and design under uncertainty with physics related applications.

Jorge Cortés received the Licenciatura degree in mathematics from Universidad de Zaragoza, Zaragoza, Spain, in 1997, and the Ph.D. degree in engineering mathematics from Universidad Carlos III de Madrid, Madrid, Spain, in 2001. He held postdoctoral positions with the University of Twente, Twente, The Netherlands, and the University of Illinois at Urbana-Champaign, Urbana, IL, USA. He was an Assistant Professor with the Department of Applied Mathematics and Statistics, University of California, Santa Cruz, CA, USA, from 2004 to 2007. He is a Professor in the Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA, USA. He is a Fellow of IEEE, SIAM, and IFAC. His research interests include distributed control and optimization, network science, nonsmooth analysis, reasoning and decision making under uncertainty, network neuroscience, and multi-agent coordination in robotic, power, and transportation networks.

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The work was supported by NSF, United States Award CMMI-1826065 (EN and JC) and ARO, United States Award W911NF-18-1-0213 (JC). RP’s stay at San Diego was funded by the Centro de Formación Interdisciplinaria Superior from Universitat Politécnica de Cataluña, Spain . The material in this paper was partially presented at the 2019 American Control Conference (ACC), July 10–12, 2019, Philadelphia, PA, USA. This paper was recommended for publication in revised form by Associate Editor Denis Efimov under the direction of Editor Daniel Liberzon.

© 2022 The Author(s). Published by Elsevier Ltd.