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

2021/09/28 by Juarez-Alvarez, Omar, Franci, Alessio
#Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Biological sciences #FOS: Mathematics #FOS: Physical sciences #Neurons and Cognition (q-bio.NC)

paper · doi:10.48550/arxiv.2109.13932

Abstract

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.

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