Pattern Formation in a Spiking Neural-Field of Renewal Neurons

TL;DR

This paper develops a mathematical framework to understand how neural patterns, specifically Turing patterns, emerge in networks of renewal spiking neurons, linking cellular properties to large-scale pattern formation.

Contribution

It introduces a PDE-based formalism for analyzing pattern formation in renewal neuron networks, providing analytical conditions for Turing instabilities.

Findings

Derived conditions for Turing instability in renewal neuron networks

Numerically identified bifurcation lines separating asynchronous and patterned states

Provided a theoretical basis connecting cellular dynamics to network-level patterns

Abstract

Elucidating the neurophysiological mechanisms underlying neural pattern formation remains an outstanding challenge in Computational Neuroscience. In this paper, we address the issue of understanding the emergence of neural patterns by considering a network of renewal neurons, a well-established class of spiking cells. Taking the thermodynamics limit, the network's dynamics can be accurately represented by a partial differential equation coupled with a nonlocal differential equation. The stationary state of the nonlocal system is determined, and a perturbation analysis is performed to analytically characterize the conditions for the occurrence of Turing instabilities. Considering neural network parameters such as the synaptic coupling and the external drive, we numerically obtain the bifurcation line that separates the asynchronous regime from the emergence of patterns. Our theoretical findings provide a new and insightful perspective on the emergence of Turing patterns in spiking neural networks. In the long term, our formalism will enable the study of neural patterns while maintaining the connections between microscopic cellular properties, network coupling, and the emergence of Turing instabilities.