Adjacency matrix; Cellular levels; Cellulars; Coupled oscillators; Feedback mechanisms; In-phase; In-phase oscillations; Network level; Network oscillations; Synaptic coupling; Control and Systems Engineering; Modeling and Simulation; Control and Optimization
Abstract :
[en] We study the emergent dynamics of a network of synaptically coupled slow-fast oscillators. Synaptic coupling provides a network-level positive feedback mechanism that cooperates with cellular-level positive feedback to ignite in-phase network oscillations. Using analytical bifurcation analysis, we prove that the Perron-Frobenius eigenvector of the network adjacency matrix fully controls the oscillation pattern locally in a neighborhood of a Hopf bifurcation. Besides shifting the focus from the spectral properties of the network Laplacian matrix to the network adjacency matrix, we discuss other key differences between synaptic and diffusive coupling.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Juarez-Alvarez, Omar; UNAM, Faculty of Sciences, Department of Mathematics, Mexico
Franci, Alessio ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Brain-Inspired Computing ; UNAM, Faculty of Sciences, Department of Mathematics, Mexico
Language :
English
Title :
In-phase oscillations from the cooperation of cellular and network positive feedback in synaptically-coupled oscillators
Publication date :
2021
Event name :
2021 60th IEEE Conference on Decision and Control (CDC)
Event place :
Austin, Usa
Event date :
13-12-2021 => 17-12-2021
Audience :
International
Main work title :
60th IEEE Conference on Decision and Control, CDC 2021
Publisher :
Institute of Electrical and Electronics Engineers Inc.
This work was supported by UNAM-DGAPA-PAPIIT grant IN102420 and by CONACyT grant A1-S-10610. 1O. P. Juarez-Alvarez is with the Department of Mathematics, Faculty of Sciences, UNAM. pat jualv@ciencias.unam.mx 2A. Franci is with the Department of Mathematics, Faculty of Sciences, UNAM, afranci@ciencias.unam.mx. 1Note that the notion of emergent dynamics used in [1], [2] is different from ours.
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