Quasilinearization-based controllability analysis of neuronal rate networks

Seul Ah Kim, Shinung Ching

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations

Abstract

Recent interest has developed around the problem of assaying the controllability of networks in the brain. The analysis of such networks is highly nontrivial, owing to their overwhelming complexity. Thus, any controllability analysis must tradeoff against model complexity/explanatory power, and analysis tractability. Here, we consider a class of neuronal network models with nearly linear dynamics, whose primary complication arises due to a sigmoidal nonlinearity in the neuronal coupling. Exploiting the equivalence between the controllability gramian and the steady state covariance matrix of a linear system under white noise, we develop an approximate controllability analysis based on the method of stochastic linearization (quasilinearization). We show that for this relatively simple system, the quasilinear approach generates a significantly better characterization of controllability as compared with a Jacobian linearization. Our results provide a new tool for assessing controllability of networks with sigmoidal interactions, and, moreover, highlight the potential inaccuracy of linear characterizations of networks with even relatively mild nonlinearities.

Original languageEnglish
Title of host publication2016 American Control Conference, ACC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages7371-7376
Number of pages6
ISBN (Electronic)9781467386821
DOIs
StatePublished - Jul 28 2016
Event2016 American Control Conference, ACC 2016 - Boston, United States
Duration: Jul 6 2016Jul 8 2016

Publication series

NameProceedings of the American Control Conference
Volume2016-July
ISSN (Print)0743-1619

Conference

Conference2016 American Control Conference, ACC 2016
Country/TerritoryUnited States
CityBoston
Period07/6/1607/8/16

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