In-phase oscillations from the cooperation of cellular and network positive feedback in synaptically-coupled oscillators

Juarez-Alvarez, Omar; Franci, Alessio

doi:10.1109/CDC45484.2021.9683708

Paper published in a book (Scientific congresses and symposiums)

In-phase oscillations from the cooperation of cellular and network positive feedback in synaptically-coupled oscillators

Juarez-Alvarez, Omar; Franci, Alessio

2021 • In 60th IEEE Conference on Decision and Control, CDC 2021

Peer reviewed

Permalink
https://hdl.handle.net/2268/303278

DOI
10.1109/CDC45484.2021.9683708

Files (1)Send to Details Statistics Bibliography Similar publications

Files

Full Text

2109.13932.pdf

Author preprint (2.85 MB)

Download

All documents in ORBi are protected by a user license.

Send to

RIS BibTex APA Chicago Permalink X Linkedin

Details

Keywords :

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.

ISBN/EAN :

978-1-66543-659-5

Peer reviewed :

Peer reviewed

Additional URL :

http://xplorestaging.ieee.org/ielx7/9682670/9682776/09683708.pdf?arnumber=9683708

Funding text :

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.

Available on ORBi :

since 26 May 2023

Statistics

Number of views

14 (0 by ULiège)

Number of downloads

11 (0 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

Bibliography

J. Kim, J. Yang, H. Shim, J. S. Kim, and J. H. Seo, "Robustness of synchronization of heterogeneous agents by strong coupling and a large number of agents, " IEEE Trans Automat Contr, vol. 61, no. 10, pp. 3096-3102, 2016.
E. Panteley and A. Loria, "Synchronization and dynamic consensus of heterogeneous networked systems, " IEEE Trans Automat Contr, vol. 62, no. 8, pp. 3758-3773, 2017.
H. Aréchiga, "Sustrato neural de los ritmos biológicos, " Mensaje Bioquímico, vol. 28, pp. 25-250, 2004.
J. A. Evans, "Collective timekeeping among cells of the master circadian clock, " J. of Endocrinol, vol. 230, pp. 27-49, 2016.
A. B. Webb, N. Angelo, J. E. Huettner, and E. D. Herzog, "Intrinsic, nondeterministic circadian rhythm generation in identified mammalian neurons, " PNAS, vol. 106, no. 38, pp. 16493-16498, 2009.
T. Noguchi, T. L. Leise, N. J. Kingsbury, T. Diemer, L. L. Wang, M. A. Henson, and D. K. Welsh, "Calcium circadian rhythmicity in suprachiasmatic nucleus: Cell autonomy and network modulation, " eNeuro, vol. 4, 7 2017.
A. L. Hodgkin and A. F. Huxley, "A quantitative description of membrane current and its application to conduction and excitation in nerve, " J Physiol, vol. 117, no. 4, pp. 500-544, 1952.
R. FitzHugh, "Mathematical models of threshold phenomena in the nerve membrane, " Bull Math Biophysics, vol. 17, pp. 257-278, 2020.
V. V. Gusev and E. V. Pribavkina, "On synchronizing colorings and the eigenvectors of digraphs, " in 41st International Symposium on Mathematical Foundations of Computer Science, MFCS, 2016.
J. Zhong, J. Lu, and D. W. C. Ho, "Controllability and synchronization analysis of identical-hierarchy mixed-value logical control networks, " IEEE Trans Cybern, vol. 47, no. 11, pp. 3482-3493, 2017.
J. G. Lee and R. Sepulchre, "Rapid synchronization under weak synaptic coupling, " in 59th IEEE Conference on Decision and Control, CDC, 2020.
F. Forni and R. Sepulchre, "Differential dissipativity theory for dominance analysis, " IEEE Transactions on Automatic Control, vol. 64, no. 6, pp. 2340-2351, 2018.
J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer, 1983.
P. D. Powell, "Calculating determinants of block matrices. " https://arxiv. org/pdf/1112. 4379v1. pdf, 2011.
A. Pavlov, N. de Wouw, and H. Nijmeijer, "Convergent systems: Analysis and synthesis, " in Control and Observer Design for Nonlinear Finite and Infinite Dimensional Systems (T. Meurer, K. Graichen, and E.-D. Gilles, eds.), pp. 131-146, Springer, 2005.
R. Frucht, "Herstellung von graphen mit vorgegebener abstrakter gruppe, " Compositio Mathematica, vol. 6, pp. 239-250, 1939.
X. Zhou, H. Feng, J. Feng, and Y. Zhao, "On synchonization of pinning-controlled networks with reducible and asymmetric coupling matrix, " Communications and Networks, vol. 3, no. 2, pp. 118-126, 2011.
D. K. Welsh, J. S. Takahashi, and S. A. Kay, "Suprachiasmatic nucleus: Cell autonomy and network properties, " Annu Rev Physiol., vol. 72, pp. 551-577, 2010.
D. DeWoskin, J. Myung, M. C. D. Belle, H. D. Piggins, T. Takumi, and D. B. Forger, "Distinct roles for gaba across multiple timescales in mammalian circadian rhythm, " PNAS, 2015.
Y. Shan, J. H. Abel, Y. Li, D. P. Olson, and J. S. Doyle, F. J. III ans Takahashi, "Dual-color single-cell imaging of the suprachiasmatic nucleus reveals a circadian role in network synchrony, " Neuron, vol. 108, pp. 1-16, 10 2020.
C. O. Diekman, M. D. C. Belle, R. P. Irwin, C. N. Allen, and H. D. Piggins, "Causes and consequences of hyperexcitation in central clock neurons, " PLoS Comput Biol, vol. 9, 2013.
M. Mieda, "The network mechanism of the central circadian pacemaker of the scn: Do avp neurons play a more critical role than expected?, " Front Neurosci., vol. 13, no. 139, 2019.
S. Varadarajan, R. Tajiri, M. ans Jain, R. Holt, Q. Ahmed, J. LeSauter, and R. Silver, "Connectome of the suprachiasmatic nucleus: New evidence of the core-shell relationship, " eNeuro, vol. 5, no. 5, 2018.