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

TL;DR

This paper investigates how synaptic and cellular positive feedback mechanisms cooperate to produce in-phase oscillations in networks of coupled oscillators, using bifurcation analysis to link network structure to oscillation patterns.

Contribution

It introduces a novel analytical approach showing the Perron-Frobenius eigenvector of the adjacency matrix controls oscillation patterns near bifurcation points.

Findings

Perron-Frobenius eigenvector determines oscillation pattern.

Synaptic coupling acts as a positive feedback mechanism.

Network adjacency matrix is key to understanding dynamics.

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.