Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Structural characterization of oscillations in brain networks with
rate dynamics
E. Nozari, R. Planas, J. Cortés
Automatica 146 (2022), 110653
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 the
linear-threshold model. Exploiting the switched-affine nature of
linear-threshold dynamics, we obtain various necessary and/or
sufficient conditions 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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Mechanical and Aerospace Engineering,
University of California, San Diego
9500 Gilman Dr,
La Jolla, California, 92093-0411
Ph: 1-858-822-7930
Fax: 1-858-822-3107
cortes at ucsd.edu
Skype id:
jorgilliyo